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simple modules

Proceedings of the Edinburgh Mathematical Society (1)

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The centralizer of a subgroup in a group algebra
Part of
- Representation theory of groups
Susanne Danz, Harald Ellers, John Murray
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 1 / February 2013

Published online by Cambridge University Press:

20 November 2012, pp. 49-56
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Let 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.