2007
DOI: 10.1016/j.jalgebra.2007.04.026
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Mackey functors, induction from restriction functors and coinduction from transfer functors

Abstract: Boltje's plus constructions extend two well-known constructions on Mackey functors, the fixed-point functor and the fixed-quotient functor. In this paper, we show that the plus constructions are induction and coinduction functors of general module theory. As an application, we construct simple Mackey functors from simple restriction functors and simple transfer functors. We also give new proofs for the classification theorem for simple Mackey functors and semisimplicity theorem of Mackey functors. © 2007 Elsev… Show more

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Cited by 9 publications
(33 citation statements)
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“…Our first main result in this direction concerns the construction of simple biset functors using the techniques in [12]. In fact our result extends to classification and description of simple modules of certain unital subalgebras.…”
Section: Introductionmentioning
confidence: 92%
See 3 more Smart Citations
“…Our first main result in this direction concerns the construction of simple biset functors using the techniques in [12]. In fact our result extends to classification and description of simple modules of certain unital subalgebras.…”
Section: Introductionmentioning
confidence: 92%
“…We shall not introduce this triangle-structure in this paper. But all of the results in [12,Section 3] hold in this case with some modifications. Furthermore it is easy to describe the coordinate modules of the functors induced (or coinduced) from these subalgebras.…”
Section: Alcahestic Subalgebras and Simple Modulesmentioning
confidence: 99%
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“…[4, Theorem 4.1] There are bijective correspondences between 1. the isomorphism classes of simple X , Y -modules, 2. the isomorphism classes of simple 0, 0 -modules,3. the isomorphism classes of simple pairs (H, V ) as H runs over all subquotients of G.We denote by SX ,Y H,Vthe simple X , Y -module corresponding to the simple pair (H, V ).…”
mentioning
confidence: 99%