A Swan length theorem and a Fong dimension theorem for Mackey algebras


Yaraneri E.

JOURNAL OF ALGEBRA, vol.311, no.1, pp.365-379, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 311 Issue: 1
  • Publication Date: 2007
  • Doi Number: 10.1016/j.jalgebra.2006.12.012
  • Title of Journal : JOURNAL OF ALGEBRA
  • Page Numbers: pp.365-379

Abstract

We first present some results about Mackey algebras of p-groups over fields of characteristic p, including their primitive idempotents and decompositions of their simple and principal indecomposable modules under restriction. We then apply these results together with a Green's indecomposability theorem for Mackey algebras to obtain Mackey algebra versions of some classical results of group algebras which are mostly related to restriction, induction and dimensions of modules. Our results about dimensions include Mackey algebra analogues of Dickson's theorem, Swan's theorem and Fong's dimension formula. (c) 2006 Elsevier Inc. All rights reserved.