## 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 μ_{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 μ_{R} (N) where N is a normal subgroup of G. Observing that 1_{N} μ_{R} (G) 1_{N} is a crossed product of G / N over μ_{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.

Original language | English |
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Pages (from-to) | 244-274 |

Number of pages | 31 |

Journal | Journal of Algebra |

Volume | 303 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Sept 2006 |

Externally published | Yes |

## Keywords

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