Methods of representation theory, with applications to finite groups and orders. Vol. I. (English) Zbl 0469.20001

Curtis, Charles W.; Reiner, Irving

Pure and Applied Mathematics. A Wiley-Interscience Publication. New York etc.: John Wiley & Sons. XXI, 819 p. £40.70 (1981).

MSC:

20-02	Research exposition (monographs, survey articles) pertaining to group theory
16-02	Research exposition (monographs, survey articles) pertaining to associative rings and algebras
20Cxx	Representation theory of groups
16H05	Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
16Gxx	Representation theory of associative rings and algebras
16U30	Divisibility, noncommutative UFDs
20C05	Group rings of finite groups and their modules (group-theoretic aspects)
20C10	Integral representations of finite groups
20C15	Ordinary representations and characters
20C20	Modular representations and characters
20C25	Projective representations and multipliers
16P10	Finite rings and finite-dimensional associative algebras

Keywords:

representation theory of finite groups; modular representation theory of finite groups; representations of finite-dimensional algebras; semisimple algebras; Dedekind domains; projective covers; injective envelopes; Krull-Schmidt-Azumaya theorem; separable algebras; splitting fields; Frobenius reciprocity; Mackey’s theorems; Clifford theory; Hecke algebras; Brauer characters; vertices; sources; Green correspondence; p- solvable groups; hereditary orders; integral representation theory; projective modules over integral group rings; orders of finite representation type; Gorenstein orders