Peer-Reviewed Journal Details
Mandatory Fields
Danz, S; Ellers, H; Murray, J
2013
February
Proceedings of the Edinburgh Mathematical Society
The centralizer of a subgroup in a group algebra
Published
4 ()
Optional Fields
56
49
56
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 FG(H). Among these, we provide examples to show that the centre Z(FG(H)) can be larger than the F-algebra generated by Z(FG) and Z(FH), FG(H) can have primitive central idempotents that are not of the form e f, where e and f are primitive central idempotents of FG and FH respectively, it is not always true that the simple FG(H)-modules are the same as the non-zero FG(H)-modules Hom(FH)(S,T down arrow H), where S and T are simple FH and FG-modules, respectively.
NEW YORK
0013-0915
10.1017/S0013091512000077
Grant Details