Representation Theory / Algebra and Applications Bd.19 (PDF)
Introducing the representation theory of groups and finite dimensional algebras, this book first studies basic non-commutative ring theory, covering the necessary background of elementary homological algebra and representations of groups to block...
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Introducing the representation theory of groups and finite dimensional algebras, this book first studies basic non-commutative ring theory, covering the necessary background of elementary homological algebra and representations of groups 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.
- Autor: Alexander Zimmermann
- 2014, 2014, 707 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319079689
- ISBN-13: 9783319079684
- Erscheinungsdatum: 15.08.2014
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
- Dateiformat: PDF
- Größe: 7.75 MB
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- Vorlesefunktion
“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)
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