Composite functors' splittings

JOURNAL OF ALGEBRA

卷:290

Article

Troesch, A

关键词: functor categories;    Taylor functors;    symmetric powers;    Ext-groups;   

DOI  :  10.1016/j.jalgebra.2005.05.001

来源: Elsevier

【 摘 要 】

A case of natural decomposition of plethysm is studied. We work within the category of functors between vector spaces over a prime field F-p. The symmetric power S circle B of a functor B is shown to split when B takes p-boolean algebras values-these are algebras whose product satisfies x(p) = x. The injective envelope of the identity functor takes such values. This is applied to functor cohomology computations, which are relevant to the study of the cohomology of Eilenberg-Mac Lane spaces. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free