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      Clifford theory for Mackey algebras

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      Author(s)
      Yaraneri, E.
      Date
      2006-09-01
      Source 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
      Article
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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 theory
      Graded algebra
      Green ’ s indecomposibility criterion
      Mackey Algebra
      Mackey Functor
      Permalink
      http://hdl.handle.net/11693/11507
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.jalgebra.2006.01.049
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      • Department of Mathematics 653
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