Some bismash products that are not group algebras II

JOURNAL OF ALGEBRA

卷:375

Article

Collins, Michael J.

关键词: Hopf algebras;    Bismash products;    Symmetric groups;    Group algebras;    Characters;    Unipotent characters;   

DOI  :  10.1016/j.jalgebra.2012.10.022

来源: Elsevier

【 摘 要 】

We consider a family of Hopf algebras, each constructed as a bismash product from a factorisation of the symmetric group S-N. These are semisimple as algebras over C and we show that they do not have the structure (as an algebra) of any group algebra if N >= 5. Previously, the author has established this in the special cases where N has the form p + 1 or p + 2 for p prime; here the general result is obtained by very different methods. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free