Universitext

Representation Theory of Finite Monoids

Authors: Steinberg, Benjamin

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  • 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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  • ISBN 978-3-319-43932-7
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Softcover $44.99
$84.99 (listprice)
price for USA in USD
valid through June 30, 2019
  • ISBN 978-3-319-43930-3
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About this Textbook

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.

About the authors

Benjamin Steinberg is a professor at City College of New York and the CUNY graduate center. Steinberg is an algebraist interested in a broad range of areas including semigroups, geometric group theory and representation theory. Other research interests include automata theory, finite state Markov chains and algebras associated to etale groupoids. Steinberg is the co-author of a 2009 Springer publication in the SMM series entitled "The q-theory of Finite Semigroups" and author of the (c) 2012 UTX "Representation Theory of Finite Groups". Ben Steinberg is also an active editorial board member of the Semigroup Forum journal.

Reviews

“The real strength of the book is that it also addresses and presents many recent applications of representation theory of finite monoids which served as motivation for many activities in the area during the last twenty years. ... this is a well-written and very timely monograph which is suitable for both advanced researchers and graduate students from a wide range of mathematical areas.” (Volodymyr Mazorchuck, Mathematical Reviews, September, 2017)

Table of contents (21 chapters)

Table of contents (21 chapters)

Buy this book

eBook $34.99
$64.99 (listprice)
price for USA in USD (gross)
valid through June 30, 2019
  • ISBN 978-3-319-43932-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $44.99
$84.99 (listprice)
price for USA in USD
valid through June 30, 2019
  • ISBN 978-3-319-43930-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Representation Theory of Finite Monoids
Authors
Series Title
Universitext
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-43932-7
DOI
10.1007/978-3-319-43932-7
Softcover ISBN
978-3-319-43930-3
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XXIV, 320
Number of Illustrations
13 b/w illustrations, 15 illustrations in colour
Topics