ISBN: 9783319439303
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles… mais…
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2016, ISBN: 3319439308
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles… mais…
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Representation Theory of Finite Monoids | Benjamin Steinberg | Taschenbuch | Universitext | Paperback | xxiv | Englisch | 2016 | Springer International Publishing | EAN 9783319439303 - Livro de bolso
2016, ISBN: 9783319439303
[ED: Taschenbuch], [PU: Springer International Publishing], This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully … mais…
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ISBN: 9783319439303
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles… mais…
2016, ISBN: 3319439308
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles… mais…
2016
ISBN: 3319439308
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles… mais…
2016, ISBN: 3319439308
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles… mais…
Representation Theory of Finite Monoids | Benjamin Steinberg | Taschenbuch | Universitext | Paperback | xxiv | Englisch | 2016 | Springer International Publishing | EAN 9783319439303 - Livro de bolso
2016, ISBN: 9783319439303
[ED: Taschenbuch], [PU: Springer International Publishing], This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully … mais…
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This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields.
Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional algebras. The content is divided into 7 parts. Part I consists of 3 preliminary chapters with no prior knowledge beyond group theory assumed. Part II forms the core of the material giving a modern module-theoretic treatment of the Clifford –Munn–Ponizovskii theory of irreducible representations. Part III concerns character theory and the character table of a monoid. Part IV is devoted to the representation theory of inverse monoids and categories and Part V presents the theory of the Rhodes radical with applications to triangularizability. Part VI features 3 chapters devoted to applications to diverse areas of mathematics and forms a high point of the text. The last part, Part VII, is concerned with advanced topics. There are also 3 appendices reviewing finite dimensional algebras, group representation theory, and Möbius inversion.Dados detalhados do livro - Representation Theory of Finite Monoids Benjamin Steinberg Author
EAN (ISBN-13): 9783319439303
ISBN (ISBN-10): 3319439308
Livro de capa dura
Livro de bolso
Ano de publicação: 2016
Editor/Editora: Springer International Publishing Core >1
Livro na base de dados desde 2016-08-16T15:43:23+01:00 (Lisbon)
Página de detalhes modificada pela última vez em 2024-03-31T09:32:23+01:00 (Lisbon)
Número ISBN/EAN: 9783319439303
Número ISBN - Ortografia alternativa:
3-319-43930-8, 978-3-319-43930-3
Ortografia alternativa e termos de pesquisa relacionados:
Autor do livro: steinberg, ben stein, benjamin, clifford
Título do livro: monoid, benjamin, mono, representation theory, steinberg, fini
Dados da editora
Autor: Benjamin Steinberg
Título: Universitext; Representation Theory of Finite Monoids
Editora: Springer; Springer International Publishing
320 Páginas
Ano de publicação: 2016-12-19
Cham; CH
Impresso / Feito em
Língua: Inglês
80,24 € (DE)
82,49 € (AT)
88,50 CHF (CH)
POD
XXIV, 320 p. 28 illus., 15 illus. in color.
BC; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Gruppen und Gruppentheorie; Verstehen; automata theory; finite monoids; monoid applications Markov chains; monoid applications automata theory; monoid applications combinatorics; monoid applications probability; representation theory finite monoids; representation theory inverse monoids; zeta function languages; monoid algebras; combinatorics; Group Theory and Generalizations; Probability Theory; Discrete Mathematics; Wahrscheinlichkeitsrechnung und Statistik; Stochastik; Diskrete Mathematik; EA
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields.
Preface.- List of Figures.- Introduction.- I. Elements of Monoid Theory.- 1. The Structure Theory of Finite Monoids.- 2. R-trivial Monoids.- 3. Inverse Monoids.- II. Irreducible Representations.- 4. Recollement: The Theory of an Idempotent.- 5. Irreducible Representations.- III. Character Theory.- 6. Grothendieck Ring.- 7. Characters and Class Functions.- IV. The Representation Theory of Inverse Monoids.- 8. Categories and Groupoids.- 9. The Representation Theory of Inverse Monoids.- V. The Rhodes Radical.- 10. Bi-ideals and R. Steinberg's Theorem.- 11. The Rhodes Radical and Triangularizability.- VI. Applications.- 12. Zeta Functions of Languages and Dynamical Systems.- 13. Transformation Monoids.- 14. Markov Chains.- VII. Advanced Topics.- 15. Self-injective, Frobenius and Symmetric Algebras.- 16. Global Dimension.- 17. Quivers of Monoid Algebras.- 18. Further Developments.- A. Finite Dimensional Algebras.- B. Group Representation Theory.- C. Incidence Algebras and Möbius Inversion.- References.- Index of Notation.- Subject Index.
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields.
Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional algebras. The content is divided into 7 parts. Part I consists of 3 preliminary chapters with no prior knowledge beyond group theory assumed. Part II forms the core of the material giving a modern module-theoretic treatment of the Clifford –Munn–Ponizovskii theory of irreducible representations. Part III concerns character theory and the character table of a monoid. Part IV is devoted to the representation theory of inverse monoids and categories and Part V presents the theory of the Rhodes radical with applications to triangularizability. Part VI features 3 chapters devoted to applications to diverse areas of mathematics and forms a high point of the text. The last part, Part VII, is concerned with advanced topics. There are also 3 appendices reviewing finite dimensional algebras, group representation theory, and Möbius inversion.
An entire part of the text is devoted to applications to Markov chains, combinatorics, and automata theory Accessible to a wide readership of graduate students and researchers, including non-experts in semigroups Contains exercises, chapter notes, and thoroughly worked examples
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