Author:
Danz Susanne,Ellers Harald,Murray John
Abstract
AbstractLet F be an algebraically closed field, G be a finite group and H be a subgroup of G. We answer several questions about the centralizer algebra FGH. Among these, we provide examples to show that•the centre Z(FGH) can be larger than the F-algebra generated by Z(FG) and Z(FH),•FGH can have primitive central idempotents that are not of the form ef, where e and f are primitive central idempotents of FG and FH respectively,•it is not always true that the simple FGH-modules are the same as the non-zero FGH-modules HomFH(S, T ↓ H), where S and T are simple FH and FG-modules, respectively.
Publisher
Cambridge University Press (CUP)
Reference12 articles.
1. Ellers H. and Murray J. , Blocks of centralizer algebras and affine Hecke algebras, submitted.
2. The defect groups of a clique, p-solvable groups, and Alperin's conjecture,;Ellers;J. Reine Angew. Math.,1995
3. GAP Group, GAP—groups, algorithms, programming—a system for computational discrete algebra, Version 4.4.10 (2007) (available at www.gap-system.org).
4. Local Representation Theory
5. Group-theoretical descriptions of ring-theoretical invariants of group algebras
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