Alexander Zimmermann: Representation Theory

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Cover: 9783319079677 | Representation Theory | A Homological Algebra Point of View | Buch

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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

Zusammenfassung

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

Includes supplementary material: [...]

Inhaltsverzeichnis

Rings, Algebras and Modules.- Modular Representations of Finite Groups.- Abelian and Triangulated Categories.- Morita theory.- Stable Module Categories.- Derived Equivalences.

Details

Erscheinungsjahr:	2014
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	728
Reihe:	Algebra and Applications
Inhalt:	xx 707 S. 59 s/w Illustr. 707 p. 59 illus.
ISBN-13:	9783319079677
ISBN-10:	3319079670
Sprache:	Englisch
Herstellernummer:	86322834
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Zimmermann, Alexander
Auflage:	2014
Hersteller:	Springer International Publishing Springer International Publishing AG Algebra and Applications
Maße:	241 x 160 x 45 mm
Von/Mit:	Alexander Zimmermann
Erscheinungsdatum:	26.08.2014
Gewicht:	1,244 kg

preigu-id: 105223301