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Representation theory of finite monoids [electronic resource]

Representation theory of finite monoids [electronic resource]

Material type
E-Book(소장)
Personal Author
Steinberg, Benjamin.
Title Statement
Representation theory of finite monoids [electronic resource] / Benjamin Steinberg.
Publication, Distribution, etc
Cham :   Springer International Publishing :   Imprint: Springer,   2016.  
Physical Medium
1 online resource (xxiv, 317 p.) : ill. (chiefly col.).
Series Statement
Universitext,0172-5939, 2191-6675 (electronic)
ISBN
9783319439327
요약
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.
General Note
Title from e-Book title page.  
Content Notes
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.
Bibliography, Etc. Note
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Monoids. Representations of groups.
Short cut
URL
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001 000046030106
005 20200605153242
006 m d
007 cr
008 200601s2016 sz a ob 001 0 eng d
020 ▼a 9783319439327
040 ▼a 211009 ▼c 211009 ▼d 211009
082 0 4 ▼a 512.55 ▼2 23
084 ▼a 512.55 ▼2 DDCK
090 ▼a 512.55
100 1 ▼a Steinberg, Benjamin.
245 1 0 ▼a Representation theory of finite monoids ▼h [electronic resource] / ▼c Benjamin Steinberg.
260 ▼a Cham : ▼b Springer International Publishing : ▼b Imprint: Springer, ▼c 2016.
300 ▼a 1 online resource (xxiv, 317 p.) : ▼b ill. (chiefly col.).
490 1 ▼a Universitext, ▼x 0172-5939, ▼x 2191-6675 (electronic)
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a 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.
520 ▼a 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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Monoids.
650 0 ▼a Representations of groups.
830 0 ▼a Universitext.
830 0 ▼a Universitext, ▼x 0172-5939.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-3-319-43932-7
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

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No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.55 Accession No. E14023050 Availability Loan can not(reference room) Due Date Make a Reservation Service M

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