Standard stratifications of El categories and Alperin's weight conjecture

JOURNAL OF ALGEBRA

卷:320

Article

Webb, Peter

关键词: Orbit category;    Category algebra;    Representation;    Alperin's weight conjecture;    Ringel dual;    Tilting module;   

DOI  :  10.1016/j.jalgebra.2006.03.052

来源: Elsevier

【 摘 要 】

We characterize the finite El categories whose representations are standardly stratified with respect to the natural preorder on the simple representations. The orbit category of a finite group with respect to any set of subgroups is always such a category. Taking the subgroups to be the p-subgroups of the group, we reformulate Alperin's weight conjecture in terms of the standard and proper costandard representations of the orbit category. We do this using the properties of the Ringel dual construction and a theorem of Dlab, which have elsewhere been described for standardly stratified algebras where there is a partial order on the simple modules. We indicate that these results hold in the generality of an algebra whose simple modules are preordered, rather than partially ordered. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free