Clifford theory for Mackey algebras
Author(s)
Date
2006-09-01Source Title
Journal of Algebra
Print ISSN
0021-8693
Electronic ISSN
1090-266X
Publisher
Academic Press
Volume
303
Issue
1
Pages
244 - 274
Language
English
Type
ArticleItem Usage Stats
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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 μR (G) be the Mackey algebra of a finite group G over a commutative unital ring R, and let 1N be the unity of μR (N) where N is a normal subgroup of G. Observing that 1N μR (G) 1N is a crossed product of G / N over μR (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. © 2006 Elsevier Inc. All rights reserved.
Keywords
Clifford theoryGraded algebra
Green ’ s indecomposibility criterion
Mackey Algebra
Mackey Functor