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The Resource Representation Theory of Finite Monoids, by Benjamin Steinberg, (electronic resource)

Representation Theory of Finite Monoids, by Benjamin Steinberg, (electronic resource)

Label
Representation Theory of Finite Monoids
Title
Representation Theory of Finite Monoids
Statement of responsibility
by Benjamin Steinberg
Creator
Subject
Language
eng
Summary
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.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Steinberg, Benjamin
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
Series statement
  • Springer eBooks
  • Universitext,
http://library.link/vocab/subjectName
  • Mathematics
  • Group theory
  • Probabilities
  • Combinatorics
Label
Representation Theory of Finite Monoids, by Benjamin Steinberg, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-43932-7
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
978-3-319-43932-7
Dimensions
unknown
Extent
1 online resource (XXIV, 320 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319439327
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-43932-7
Other physical details
28 illustrations, 15 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)967721605
Label
Representation Theory of Finite Monoids, by Benjamin Steinberg, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-43932-7
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
978-3-319-43932-7
Dimensions
unknown
Extent
1 online resource (XXIV, 320 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319439327
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-43932-7
Other physical details
28 illustrations, 15 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)967721605

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