Representation Theory of Finite Groups / Steinberg, Benjamin (2012)  

Público ISBD Título : Representation Theory of Finite Groups : An Introductory Approach Tipo de documento: documento electrónico Autores: Steinberg, Benjamin ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Universitext, ISSN 0172-5939 Número de páginas: XIII, 157 p. 4 illus Il.: online resource ISBN/ISSN/DL: 978-1-4614-0776-8 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebra  Group  theory  Theory  and  Generalizations Clasificación: 51 Matemáticas Resumen: Representation Theory of Finite Groups presents group representation theory at a level accessible to advanced undergraduate students and beginning graduate students. The required background is maintained to the level of linear algebra, group theory, and very basic ring theory and avoids prerequisites in analysis and topology by dealing exclusively with finite groups. Module theory and Wedderburn theory, as well as tensor products, are deliberately omitted. Instead, an approach based on discrete Fourier Analysis is taken, thereby demanding less background from the reader. The main topics covered in this text include character theory, the group algebra and Fourier analysis, Burnside's pq-theorem and the dimension theorem, permutation representations, induced representations and Mackey's theorem, and the representation theory of the symmetric group. For those students who have an elementary knowledge of probability and statistics, a chapter on random walks on finite groups serves as an illustration to link finite stochastics and representation theory. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject and the author provides motivation and a gentle style throughout the text. A number of exercises add greater dimension to the understanding of the subject and some aspects of a combinatorial nature are clearly shown in diagrams. This text will engage a broad readership due to the significance of representation theory in diverse branches of mathematics, engineering, and physics, to name a few. Its primary intended use is as a one semester textbook for a third or fourth year undergraduate course or an introductory graduate course on group representation theory. The content can also be of use as a reference to researchers in all areas of mathematics, statistics, and several mathematical sciences En línea: http://dx.doi.org/10.1007/978-1-4614-0776-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32746 Representation Theory of Finite Groups : An Introductory Approach [documento electrónico] / Steinberg, Benjamin ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2012 . - XIII, 157 p. 4 illus : online resource. - (Universitext, ISSN 0172-5939) . ISBN : 978-1-4614-0776-8 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebra  Group  theory  Theory  and  Generalizations Clasificación: 51 Matemáticas Resumen: Representation Theory of Finite Groups presents group representation theory at a level accessible to advanced undergraduate students and beginning graduate students. The required background is maintained to the level of linear algebra, group theory, and very basic ring theory and avoids prerequisites in analysis and topology by dealing exclusively with finite groups. Module theory and Wedderburn theory, as well as tensor products, are deliberately omitted. Instead, an approach based on discrete Fourier Analysis is taken, thereby demanding less background from the reader. The main topics covered in this text include character theory, the group algebra and Fourier analysis, Burnside's pq-theorem and the dimension theorem, permutation representations, induced representations and Mackey's theorem, and the representation theory of the symmetric group. For those students who have an elementary knowledge of probability and statistics, a chapter on random walks on finite groups serves as an illustration to link finite stochastics and representation theory. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject and the author provides motivation and a gentle style throughout the text. A number of exercises add greater dimension to the understanding of the subject and some aspects of a combinatorial nature are clearly shown in diagrams. This text will engage a broad readership due to the significance of representation theory in diverse branches of mathematics, engineering, and physics, to name a few. Its primary intended use is as a one semester textbook for a third or fourth year undergraduate course or an introductory graduate course on group representation theory. The content can also be of use as a reference to researchers in all areas of mathematics, statistics, and several mathematical sciences En línea: http://dx.doi.org/10.1007/978-1-4614-0776-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32746

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The q-theory of Finite Semigroups / Rhodes, John (2009)  

Público ISBD Título : The q-theory of Finite Semigroups Tipo de documento: documento electrónico Autores: Rhodes, John ; SpringerLink (Online service) ; Steinberg, Benjamin Editorial: Boston, MA : Springer US Fecha de publicación: 2009 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XXII, 666 p Il.: online resource ISBN/ISSN/DL: 978-0-387-09781-7 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  logic  Algebra  Group  theory  Ordered  algebraic  structures  Theory  and  Generalizations  Order,  Lattices,  Algebraic  Structures  General  Systems  Logic  Formal  Languages Clasificación: 51 Matemáticas Resumen: Discoveries in finite semigroups have influenced several mathematical fields, including theoretical computer science, tropical algebra via matrix theory with coefficients in semirings, and other areas of modern algebra. This comprehensive, encyclopedic text will provide the reader – from the graduate student to the researcher/practitioner – with a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. Key features: * Develops q-theory, a new theory that provides a unifying approach to finite semigroup theory via quantization; * Contains the only contemporary exposition of the complete theory of the complexity of finite semigroups; * Introduces spectral theory into finite semigroup theory; * Develops the theory of profinite semigroups from first principles, making connections with spectra of Boolean algebras of regular languages; * Presents over 70 research problems, most new, and hundreds of exercises. Additional features: * For newcomers, an appendix on elementary finite semigroup theory; * Extensive bibliography and index. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, and thereby updates and modernizes the literature of semigroup theory Nota de contenido: I The q operator and Pseudovarieties of Relational Morphisms -- Foundations for Finite Semigroup Theory -- The q-operator -- The Equational Theory -- II Complexity in Finite Semigroup Theory -- The Complexity of Finite Semigroups -- Two-Sided Complexity and the Complexity of Operators -- III The Algebraic Lattice of Semigroup Pseudovarieties -- Algebraic Lattices, Continuous Lattices and Closure Operators -- The Abstract Spectral Theory of PV -- IV Quantales Idempotent Semirings Matrix Algebras and the Triangular Product -- Quantales -- The Triangular Product and Decomposition Results for Semirings En línea: http://dx.doi.org/10.1007/b104443 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33832 The q-theory of Finite Semigroups [documento electrónico] / Rhodes, John ; SpringerLink (Online service) ; Steinberg, Benjamin . - Boston, MA : Springer US, 2009 . - XXII, 666 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) . ISBN : 978-0-387-09781-7 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  logic  Algebra  Group  theory  Ordered  algebraic  structures  Theory  and  Generalizations  Order,  Lattices,  Algebraic  Structures  General  Systems  Logic  Formal  Languages Clasificación: 51 Matemáticas Resumen: Discoveries in finite semigroups have influenced several mathematical fields, including theoretical computer science, tropical algebra via matrix theory with coefficients in semirings, and other areas of modern algebra. This comprehensive, encyclopedic text will provide the reader – from the graduate student to the researcher/practitioner – with a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. Key features: * Develops q-theory, a new theory that provides a unifying approach to finite semigroup theory via quantization; * Contains the only contemporary exposition of the complete theory of the complexity of finite semigroups; * Introduces spectral theory into finite semigroup theory; * Develops the theory of profinite semigroups from first principles, making connections with spectra of Boolean algebras of regular languages; * Presents over 70 research problems, most new, and hundreds of exercises. Additional features: * For newcomers, an appendix on elementary finite semigroup theory; * Extensive bibliography and index. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, and thereby updates and modernizes the literature of semigroup theory Nota de contenido: I The q operator and Pseudovarieties of Relational Morphisms -- Foundations for Finite Semigroup Theory -- The q-operator -- The Equational Theory -- II Complexity in Finite Semigroup Theory -- The Complexity of Finite Semigroups -- Two-Sided Complexity and the Complexity of Operators -- III The Algebraic Lattice of Semigroup Pseudovarieties -- Algebraic Lattices, Continuous Lattices and Closure Operators -- The Abstract Spectral Theory of PV -- IV Quantales Idempotent Semirings Matrix Algebras and the Triangular Product -- Quantales -- The Triangular Product and Decomposition Results for Semirings En línea: http://dx.doi.org/10.1007/b104443 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33832

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