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Article Dans Une Revue Algebras and Representation Theory Année : 2017

On the Projective Dimensions of Mackey Functors

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Résumé

We examine the projective dimensions of Mackey functors and cohomological Mackey functors. We show over a field of characteristic p that cohomological Mackey functors are Gorenstein if and only if Sylow p-subgroups are cyclic or dihedral, and they have finite global dimension if and only if the group order is invertible or Sylow subgroups are cyclic of order 2. By contrast, we show that the only Mackey functors of finite projective dimension over a field are projective. This allows us to give a new proof of a theorem of Greenlees on the projective dimension of Mackey functors over a Dedekind domain. We conclude by completing work of Arnold on the global dimension of cohomological Mackey functors over a''.

Dates et versions

hal-03621752 , version 1 (28-03-2022)

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Serge Bouc, Radu Stancu, Peter Webb. On the Projective Dimensions of Mackey Functors. Algebras and Representation Theory, 2017, 20 (6), pp.1467-1481. ⟨10.1007/s10468-017-9695-y⟩. ⟨hal-03621752⟩
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