Clifford theory for Mackey algebras

Ergün Yaraneri*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)244-274
Number of pages31
JournalJournal of Algebra
Volume303
Issue number1
DOIs
Publication statusPublished - 1 Sept 2006
Externally publishedYes

Keywords

  • Clifford theory
  • Graded algebra
  • Green's indecomposibility criterion
  • Mackey algebra
  • Mackey functor

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