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Título : Algebraic Operads Tipo de documento: documento electrónico Autores: Loday, Jean-Louis ; SpringerLink (Online service) ; Vallette, Bruno Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, ISSN 0072-7830 num. 346 Número de páginas: XXIV, 636 p Il.: online resource ISBN/ISSN/DL: 978-3-642-30362-3 Idioma : Inglés (eng) Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Nonassociative rings Rings (Algebra) Algebraic topology Manifolds Complex manifolds Theory, Algebra Non-associative and Algebras Topology Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: In many areas of mathematics some “higher operations” are arising. These have become so important that several research projects refer to such expressions. Higher operations form new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the HomotopyTransfer Theorem. Although the necessary notions of algebra are recalled, readers areexpected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After an elementary chapter on classical algebra, accessible to undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers. Nota de contenido: Preface -- 1.Algebras, coalgebras, homology -- 2.Twisting morphisms -- 3.Koszul duality for associative algebras -- 4.Methods to prove Koszulity of an algebra -- 5.Algebraic operad -- 6 Operadic homological algebra -- 7.Koszul duality of operads -- 8.Methods to prove Koszulity of an operad -- 9.The operads As and A\infty -- 10.Homotopy operadic algebras -- 11.Bar and cobar construction of an algebra over an operad -- 12.(Co)homology of algebras over an operad -- 13.Examples of algebraic operads -- Apendices: A.The symmetric group -- B.Categories -- C.Trees -- References -- Index -- List of Notation En línea: http://dx.doi.org/10.1007/978-3-642-30362-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32989 Algebraic Operads [documento electrónico] / Loday, Jean-Louis ; SpringerLink (Online service) ; Vallette, Bruno . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012 . - XXIV, 636 p : online resource. - (Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, ISSN 0072-7830; 346) .
ISBN : 978-3-642-30362-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Nonassociative rings Rings (Algebra) Algebraic topology Manifolds Complex manifolds Theory, Algebra Non-associative and Algebras Topology Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: In many areas of mathematics some “higher operations” are arising. These have become so important that several research projects refer to such expressions. Higher operations form new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the HomotopyTransfer Theorem. Although the necessary notions of algebra are recalled, readers areexpected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After an elementary chapter on classical algebra, accessible to undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers. Nota de contenido: Preface -- 1.Algebras, coalgebras, homology -- 2.Twisting morphisms -- 3.Koszul duality for associative algebras -- 4.Methods to prove Koszulity of an algebra -- 5.Algebraic operad -- 6 Operadic homological algebra -- 7.Koszul duality of operads -- 8.Methods to prove Koszulity of an operad -- 9.The operads As and A\infty -- 10.Homotopy operadic algebras -- 11.Bar and cobar construction of an algebra over an operad -- 12.(Co)homology of algebras over an operad -- 13.Examples of algebraic operads -- Apendices: A.The symmetric group -- B.Categories -- C.Trees -- References -- Index -- List of Notation En línea: http://dx.doi.org/10.1007/978-3-642-30362-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32989 Ejemplares
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Título : Advanced Algebra : Along with a companion volume Basic Algebra Tipo de documento: documento electrónico Autores: Knapp, Anthony W ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2008 Otro editor: Imprint: Birkhäuser Colección: Cornerstones Número de páginas: XXV, 730 p. 46 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4613-4 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry Category theory (Mathematics) Homological algebra Field (Physics) Nonassociative rings Rings (Algebra) Number Non-associative and Algebras Theory Polynomials Geometry Theory, Clasificación: 51 Matemáticas Resumen: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Advanced Algebra: *Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in Basic Algebra *Chapters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, and algebraic geometry *Sections in two chapters relate the theory to the subject of Gröbner bases, the foundation for handling systems of polynomial equations in computer applications *Text emphasizes connections between algebra and other branches of mathematics, particularly topology and complex analysis *Book carries on two prominent themes recurring in Basic Algebra: the analogy between integers and polynomials in one variable over a field, and the relationship between number theory and geometry *Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems *The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that illuminate aspects of the text and introduce additional topics Advanced Algebra presents its subject matter in a forward-looking way that takes into account the historical development of the subject. It is suitable as a text for the more advanced parts of a two-semester first-year graduate sequence in algebra. It requires of the reader only a familiarity with the topics developed in Basic Algebra Nota de contenido: Transition to Modern Number Theory -- Wedderburn–Artin Ring Theory -- Brauer Group -- Homological Algebra -- Three Theorems in Algebraic Number Theory -- Reinterpretation with Adeles and Ideles -- Infinite Field Extensions -- Background for Algebraic Geometry -- The Number Theory of Algebraic Curves -- Methods of Algebraic Geometry En línea: http://dx.doi.org/10.1007/978-0-8176-4613-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34266 Advanced Algebra : Along with a companion volume Basic Algebra [documento electrónico] / Knapp, Anthony W ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2008 . - XXV, 730 p. 46 illus : online resource. - (Cornerstones) .
ISBN : 978-0-8176-4613-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry Category theory (Mathematics) Homological algebra Field (Physics) Nonassociative rings Rings (Algebra) Number Non-associative and Algebras Theory Polynomials Geometry Theory, Clasificación: 51 Matemáticas Resumen: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Advanced Algebra: *Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in Basic Algebra *Chapters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, and algebraic geometry *Sections in two chapters relate the theory to the subject of Gröbner bases, the foundation for handling systems of polynomial equations in computer applications *Text emphasizes connections between algebra and other branches of mathematics, particularly topology and complex analysis *Book carries on two prominent themes recurring in Basic Algebra: the analogy between integers and polynomials in one variable over a field, and the relationship between number theory and geometry *Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems *The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that illuminate aspects of the text and introduce additional topics Advanced Algebra presents its subject matter in a forward-looking way that takes into account the historical development of the subject. It is suitable as a text for the more advanced parts of a two-semester first-year graduate sequence in algebra. It requires of the reader only a familiarity with the topics developed in Basic Algebra Nota de contenido: Transition to Modern Number Theory -- Wedderburn–Artin Ring Theory -- Brauer Group -- Homological Algebra -- Three Theorems in Algebraic Number Theory -- Reinterpretation with Adeles and Ideles -- Infinite Field Extensions -- Background for Algebraic Geometry -- The Number Theory of Algebraic Curves -- Methods of Algebraic Geometry En línea: http://dx.doi.org/10.1007/978-0-8176-4613-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34266 Ejemplares
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Título : Algebraic Geometry and Number Theory : In Honor of Vladimir Drinfeld’s 50th Birthday Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Ginzburg, Victor Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2006 Colección: Progress in Mathematics num. 253 Número de páginas: XX, 644 p. 19 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4532-8 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Group theory Nonassociative rings Rings (Algebra) Special functions Number Physics Theory Geometry Mathematical Methods in Non-associative and Algebras Generalizations Functions Clasificación: 51 Matemáticas Resumen: One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups. These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory. Contributors: A. Eskin, V.V. Fock, E. Frenkel, D. Gaitsgory, V. Ginzburg, A.B. Goncharov, E. Hrushovski, Y. Ihara, D. Kazhdan, M. Kisin, I. Krichever, G. Laumon, Yu.I. Manin, A. Okounkov, V. Schechtman, and M.A. Tsfasman Nota de contenido: Pillowcases and quasimodular forms -- Cluster ?-varieties, amalgamation, and Poisson—Lie groups -- Local geometric Langlands correspondence and affine Kac-Moody algebras -- Integration in valued fields -- On the Euler-Kronecker constants of global fields and primes with small norms -- Asymptotic behaviour of the Euler-Kronecker constant -- Crystalline representations and F-crystals -- Integrable linear equations and the Riemann-Schottky problem -- Fibres de Springer et jacobiennes compactifiées -- Iterated integrals of modular forms and noncommutative modular symbols -- Structures membranaires En línea: http://dx.doi.org/10.1007/978-0-8176-4532-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34883 Algebraic Geometry and Number Theory : In Honor of Vladimir Drinfeld’s 50th Birthday [documento electrónico] / SpringerLink (Online service) ; Ginzburg, Victor . - Boston, MA : Birkhäuser Boston, 2006 . - XX, 644 p. 19 illus : online resource. - (Progress in Mathematics; 253) .
ISBN : 978-0-8176-4532-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Group theory Nonassociative rings Rings (Algebra) Special functions Number Physics Theory Geometry Mathematical Methods in Non-associative and Algebras Generalizations Functions Clasificación: 51 Matemáticas Resumen: One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups. These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory. Contributors: A. Eskin, V.V. Fock, E. Frenkel, D. Gaitsgory, V. Ginzburg, A.B. Goncharov, E. Hrushovski, Y. Ihara, D. Kazhdan, M. Kisin, I. Krichever, G. Laumon, Yu.I. Manin, A. Okounkov, V. Schechtman, and M.A. Tsfasman Nota de contenido: Pillowcases and quasimodular forms -- Cluster ?-varieties, amalgamation, and Poisson—Lie groups -- Local geometric Langlands correspondence and affine Kac-Moody algebras -- Integration in valued fields -- On the Euler-Kronecker constants of global fields and primes with small norms -- Asymptotic behaviour of the Euler-Kronecker constant -- Crystalline representations and F-crystals -- Integrable linear equations and the Riemann-Schottky problem -- Fibres de Springer et jacobiennes compactifiées -- Iterated integrals of modular forms and noncommutative modular symbols -- Structures membranaires En línea: http://dx.doi.org/10.1007/978-0-8176-4532-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34883 Ejemplares
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Título : Automorphic Forms and Lie Superalgebras Tipo de documento: documento electrónico Autores: Ray, Urmie ; SpringerLink (Online service) Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2006 Colección: Algebra and Applications, ISSN 1572-5553 num. 5 Número de páginas: X, 278 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-5010-7 Idioma : Inglés (eng) Palabras clave: Mathematics Nonassociative rings Rings (Algebra) Number theory Non-associative and Algebras Theory Clasificación: 51 Matemáticas Resumen: A principal ingredient in the proof of the Moonshine Theorem, connecting the Monster group to modular forms, is the infinite dimensional Lie algebra of physical states of a chiral string on an orbifold of a 26 dimensional torus, called the Monster Lie algebra. It is a Borcherds-Kac-Moody Lie algebra with Lorentzian root lattice; and has an associated automorphic form having a product expansion describing its structure. Lie superalgebras are generalizations of Lie algebras, useful for depicting supersymmetry – the symmetry relating fermions and bosons. Most known examples of Lie superalgebras with a related automorphic form such as the Fake Monster Lie algebra whose reflection group is given by the Leech lattice arise from (super)string theory and can be derived from lattice vertex algebras. The No-Ghost Theorem from dual resonance theory and a conjecture of Berger-Li-Sarnak on the eigenvalues of the hyperbolic Laplacian provide strong evidence that they are of rank at most 26. The aim of this book is to give the reader the tools to understand the ongoing classification and construction project of this class of Lie superalgebras and is ideal for a graduate course. The necessary background is given within chapters or in appendices Nota de contenido: Borcherds-Kac-Moody Lie Superalgebras -- Singular Theta Transforms of Vector Valued Modular Forms -- ?-Graded Vertex Algebras -- Lorentzian BKM Algebras En línea: http://dx.doi.org/10.1007/978-1-4020-5010-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34897 Automorphic Forms and Lie Superalgebras [documento electrónico] / Ray, Urmie ; SpringerLink (Online service) . - Dordrecht : Springer Netherlands, 2006 . - X, 278 p : online resource. - (Algebra and Applications, ISSN 1572-5553; 5) .
ISBN : 978-1-4020-5010-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Nonassociative rings Rings (Algebra) Number theory Non-associative and Algebras Theory Clasificación: 51 Matemáticas Resumen: A principal ingredient in the proof of the Moonshine Theorem, connecting the Monster group to modular forms, is the infinite dimensional Lie algebra of physical states of a chiral string on an orbifold of a 26 dimensional torus, called the Monster Lie algebra. It is a Borcherds-Kac-Moody Lie algebra with Lorentzian root lattice; and has an associated automorphic form having a product expansion describing its structure. Lie superalgebras are generalizations of Lie algebras, useful for depicting supersymmetry – the symmetry relating fermions and bosons. Most known examples of Lie superalgebras with a related automorphic form such as the Fake Monster Lie algebra whose reflection group is given by the Leech lattice arise from (super)string theory and can be derived from lattice vertex algebras. The No-Ghost Theorem from dual resonance theory and a conjecture of Berger-Li-Sarnak on the eigenvalues of the hyperbolic Laplacian provide strong evidence that they are of rank at most 26. The aim of this book is to give the reader the tools to understand the ongoing classification and construction project of this class of Lie superalgebras and is ideal for a graduate course. The necessary background is given within chapters or in appendices Nota de contenido: Borcherds-Kac-Moody Lie Superalgebras -- Singular Theta Transforms of Vector Valued Modular Forms -- ?-Graded Vertex Algebras -- Lorentzian BKM Algebras En línea: http://dx.doi.org/10.1007/978-1-4020-5010-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34897 Ejemplares
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Título : Eléments de Mathématique. Groupes et algèbres de Lie : Chapitres 2 et 3 Tipo de documento: documento electrónico Autores: N. Bourbaki ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Número de páginas: 314 p Il.: online resource ISBN/ISSN/DL: 978-3-540-33978-6 Idioma : Francés (fre) Palabras clave: Mathematics Nonassociative rings Rings (Algebra) Topological groups Lie Groups, Groups Non-associative and Algebras Clasificación: 51 Matemáticas Resumen: Groupes et algèbres de Lie, Chapitres 2 et 3 Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce deuxième volume du Livre sur les Groupes et algèbres de Lie, neuvième Livre du traité, comprend les chapitres : 2. Algèbres de Lie libres ; 3. Groupes de Lie. Le chapitre 2 poursuit la présentation des notions fondamentales des algèbres de Lie avec l’introduction des algèbres de Lie libres et de la série de Hausdorff. Le chapitre 3 est consacré aux concepts de base pour les groupes de Lies sur un corps archimédien ou ultramétrique. Ce volume contient également de notes historiques pour les chapitres 1 à 3. Ce volume est une réimpression de l’édition de 1972 En línea: http://dx.doi.org/10.1007/978-3-540-33978-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34966 Eléments de Mathématique. Groupes et algèbres de Lie : Chapitres 2 et 3 [documento electrónico] / N. Bourbaki ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - 314 p : online resource.
ISBN : 978-3-540-33978-6
Idioma : Francés (fre)
Palabras clave: Mathematics Nonassociative rings Rings (Algebra) Topological groups Lie Groups, Groups Non-associative and Algebras Clasificación: 51 Matemáticas Resumen: Groupes et algèbres de Lie, Chapitres 2 et 3 Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce deuxième volume du Livre sur les Groupes et algèbres de Lie, neuvième Livre du traité, comprend les chapitres : 2. Algèbres de Lie libres ; 3. Groupes de Lie. Le chapitre 2 poursuit la présentation des notions fondamentales des algèbres de Lie avec l’introduction des algèbres de Lie libres et de la série de Hausdorff. Le chapitre 3 est consacré aux concepts de base pour les groupes de Lies sur un corps archimédien ou ultramétrique. Ce volume contient également de notes historiques pour les chapitres 1 à 3. Ce volume est une réimpression de l’édition de 1972 En línea: http://dx.doi.org/10.1007/978-3-540-33978-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34966 Ejemplares
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