Algebra and Applications

Representation Theory

A Homological Algebra Point of View

Authors: Zimmermann, Alexander

  • Provides full proofs of key statements in the modular representation theory of groups
  • Contains a coherent treatment and full proofs of the main results on equivalences between derived categories
  • Introduces stable categories and different types of equivalences between them as well as their respective invariants
  • Is completely self-contained and only assumes a basic knowledge of algebra
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eBook $109.00
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  • ISBN 978-3-319-07968-4
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Hardcover $149.00
price for USA
  • ISBN 978-3-319-07967-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 28, 2016
  • ISBN 978-3-319-35261-9
  • Free shipping for individuals worldwide
Rent the ebook  
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About this book

Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field.

Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced.

Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.

About the authors

Alexander Zimmermann works on equivalences between derived module categories, stable module categories, Hochschild cohomology and integral and modular representations of groups.

Reviews

“The focus of this text is the representation theory of associative algebras and the modular representation theory of finite groups, with an emphasis on the interplay between these two fields. … the text at hand is aimed at a beginning graduate student without prior exposure to homological algebra. … Overall, this book is a great repository of theory, developed almost from scratch, with detailed proofs.” (Alex S. Dugas, Mathematical Reviews, May, 2016)

“This book is intended as a text for first year master students who want to specialize on representation theory, more precisely: representations of finite-dimensional algebras and modular group representations, with special emphasis on homological methods.” (Wolfgang Rump, zbMATH 1306.20001, 2015)

“The author’s intent is to provide an obviously very serious ‘introduction to the representation theory of finite groups and finite dimensional algebras via homological algebra.’ … Zimmermann’s book is geared to initiates and serious algebraists aiming at research in the indicated area. It is clearly a labor of love and fine scholarship, and should succeed in providing guidance and instruction in a most interesting and intricate subject.” (Michael Berg, MAA Reviews, October, 2014)

Table of contents (6 chapters)

  • Rings, Algebras and Modules

    Zimmermann, Alexander

    Pages 1-153

  • Modular Representations of Finite Groups

    Zimmermann, Alexander

    Pages 155-257

  • Abelian and Triangulated Categories

    Zimmermann, Alexander

    Pages 259-385

  • Morita Theory

    Zimmermann, Alexander

    Pages 387-425

  • Stable Module Categories

    Zimmermann, Alexander

    Pages 427-555

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-319-07968-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-319-07967-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 28, 2016
  • ISBN 978-3-319-35261-9
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Representation Theory
Book Subtitle
A Homological Algebra Point of View
Authors
Series Title
Algebra and Applications
Series Volume
19
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
Distribution Rights
Distribution rights In India: Ane Books India, New Delhi, India
eBook ISBN
978-3-319-07968-4
DOI
10.1007/978-3-319-07968-4
Hardcover ISBN
978-3-319-07967-7
Softcover ISBN
978-3-319-35261-9
Series ISSN
1572-5553
Edition Number
1
Number of Pages
XX, 707
Number of Illustrations and Tables
59 b/w illustrations
Topics