| 000 | 02570 a2200337 4500 | ||
|---|---|---|---|
| 020 | _a9783319079684 (electronic bk.) | ||
| 020 | _a3319079689 (electronic bk.) | ||
| 020 | _a3319079670 (print) | ||
| 020 | _a9783319079677 (print) | ||
| 024 | 7 | _a10.1007/978-3-319-07968-4 | |
| 035 | _a(OCoLC)889327917 | ||
| 050 | 4 | _aQA169 | |
| 082 | 0 | 4 | _a512.64 |
| 090 |
_c31663 _d31663 |
||
| 100 | 1 | _aZimmermann, Alexander | |
| 546 | _aeng | ||
| 245 | 1 | 0 |
_aRepresentation theory : _bA homological algebra point of view _cAlexander Zimmermann |
| 260 |
_aHeidelberg _bSpringer _c2014 |
||
| 300 |
_axx, 707 p. _bill _c25 cm |
||
| 490 | 1 |
_aAlgebra and Applications _x1572-5553 _vvol. 19 |
|
| 500 | _aBibliografie la sfarsitul capitolelor Index p. 697 | ||
| 505 | 0 | _aRings, Algebras and Modules -- Modular Representations of Finite Groups -- Abelian and Triangulated Categories -- Morita theory -- Stable Module Categories -- Derived Equivalences. | |
| 520 | _aIntroducing 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. | ||
| 650 | 2 | 4 | _aAssociative Rings and Algebras. |
| 650 | 2 | 4 | _aCategory Theory, Homological Algebra. |
| 650 | 2 | 4 | _aGroup Theory and Generalizations. |
| 650 | 7 | _aMATHEMATICS / Algebra / Intermediate | |
| 650 | 7 | _aHomological algebra | |
| 650 | 7 | _aRepresentations of algebras | |
| 942 |
_aIMAR _cCART _k512.64 _sEP |
||
| 999 |
_c31224 _d31224 |
||