The Resource Representation Theory of Finite Monoids, by Benjamin Steinberg, (electronic resource)
Representation Theory of Finite Monoids, by Benjamin Steinberg, (electronic resource)
Resource Information
The item Representation Theory of Finite Monoids, by Benjamin Steinberg, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Representation Theory of Finite Monoids, by Benjamin Steinberg, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 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 moduletheoretic 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 moduletheoretic 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.
 Language
 eng
 Extent
 1 online resource (XXIV, 320 pages)
 Contents

 Preface
 List of Figures
 Introduction
 I. Elements of Monoid Theory
 1. The Structure Theory of Finite Monoids
 2. Rtrivial 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. Biideals 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. Selfinjective, 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
 Isbn
 9783319439327
 Label
 Representation Theory of Finite Monoids
 Title
 Representation Theory of Finite Monoids
 Statement of responsibility
 by Benjamin Steinberg
 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 moduletheoretic 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 moduletheoretic 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.
 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)
 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. Rtrivial 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. Biideals 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. Selfinjective, 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
 9783319439327
 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, noncommercial 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
 10.1007/9783319439327
 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)
 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. Rtrivial 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. Biideals 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. Selfinjective, 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
 9783319439327
 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, noncommercial 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
 10.1007/9783319439327
 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/RepresentationTheoryofFiniteMonoidsby/GTpul_R5r4k/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/RepresentationTheoryofFiniteMonoidsby/GTpul_R5r4k/">Representation Theory of Finite Monoids, by Benjamin Steinberg, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>