Representations and cohomology. I: Basic representation theory of finite groups and associative algebras. (English) Zbl 0908.20001

Benson, D. J.

Cambridge Studies in Advanced Mathematics. 30. Cambridge: Cambridge University Press. xi, 246 p. (1998).

See the joined review Zbl 0908.20002 below. For a review of the first ed. (1991) see Zbl 0718.20001.

MSC:

20-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory
20C20	Modular representations and characters
20J06	Cohomology of groups
20C05	Group rings of finite groups and their modules (group-theoretic aspects)
16-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras
16G70	Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
20-02	Research exposition (monographs, survey articles) pertaining to group theory
19A22	Frobenius induction, Burnside and representation rings
20J05	Homological methods in group theory
16S34	Group rings
20C11	\(p\)-adic representations of finite groups
16Gxx	Representation theory of associative rings and algebras

Keywords:

group algebras; vertices; sources; Green correspondence; finite-dimensional algebras; hereditary algebras; path algebras; quivers; indecomposable representations; representation type; Auslander-Reiten sequences; Auslander-Reiten quivers; Burnside rings; Grothendieck rings; induction theorems; representation rings; Cartan matrices; defect groups; Brauer’s three main theorems; blocks

Citations:

Zbl 0731.20001; Zbl 0908.20002; Zbl 0718.20001