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

Yaraneri E.

JOURNAL OF ALGEBRA, cilt.311, sa.1, ss.365-379, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 311 Sayı: 1
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1016/j.jalgebra.2006.12.012
  • Dergi Adı: JOURNAL OF ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.365-379
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

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.