Clifford theory for Mackey algebras


Yaraneri E.

JOURNAL OF ALGEBRA, vol.303, no.1, pp.244-274, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 303 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.1016/j.jalgebra.2006.01.049
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.244-274
  • Istanbul Technical University Affiliated: No

Abstract

We develop a Clifford theory for Mackey algebras. For simple Mackey functors, using their classification we prove Mackey algebra versions of Clifford's theorem and the Clifford correspondence. Let mu(R)(G) be the Mackey algebra of a finite group G over a commutative unital ring R, and let 1(N) be the unity of mu(R)(N) where N is a normal subgroup of G. Observing that 1(N)mu(R)(G)1(N) is a crossed product of G/N over mu R(N), a number of results concerning group graded algebras are extended to the context of Mackey algebras, including Fong's theorem, Green's indecomposibility theorem and some reduction and extension techniques for indecomposable Mackey functors. (c) 2006 Elsevier Inc. All rights reserved.