Modular centralizer algebras corresponding to p-groups

JOURNAL OF ALGEBRA

卷:339

Article

Allan, Adam

关键词: Centralizer algebra;    Hecke algebra;    Loewy series;    Radical series;    Nilpotency index;   

DOI  :  10.1016/j.jalgebra.2011.04.026

来源: Elsevier

【 摘 要 】

We study the Loewy structure of the centralizer algebra kP(Q) for P a p-group with subgroup Q and k a field of characteristic p. Here kP(Q) is a special type of Hecke algebra. The main tool we employ is the decomposition kP(Q) = kC(P)(Q) x I of kP(Q) as a split extension of a nilpotent ideal I by the group algebra kC(P)(Q). We compute the Loewy structure for several classes of groups, investigate the symmetry of the Loewy series, and give upper and lower bounds on the Loewy length of kPQ. Several of these results were discovered through the use of MAGMA, especially the general pattern for most of our computations. As a final application of the decomposition, we determine the representation type of kPQ. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free