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1 results

  • The centralizer of a subgroup in a group algebra

  • Part of
  • 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
    • Article
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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.