9783319079677-3319079670-Representation Theory: A Homological Algebra Point of View (Algebra and Applications (19))

Representation Theory: A Homological Algebra Point of View (Algebra and Applications (19))

ISBN-13: 9783319079677
ISBN-10: 3319079670
Edition: 2014
Author: Zimmermann, Alexander
Publication date: 2014
Publisher: Springer
Format: Hardcover 727 pages
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Book details

ISBN-13: 9783319079677
ISBN-10: 3319079670
Edition: 2014
Author: Zimmermann, Alexander
Publication date: 2014
Publisher: Springer
Format: Hardcover 727 pages

Summary

Acknowledged authors Zimmermann, Alexander wrote Representation Theory: A Homological Algebra Point of View (Algebra and Applications (19)) comprising 727 pages back in 2014. Textbook and eTextbook are published under ISBN 3319079670 and 9783319079677. Since then Representation Theory: A Homological Algebra Point of View (Algebra and Applications (19)) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

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.

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