On the Projective Dimensions of Mackey Functors

Serge Bouc, Radu Stancu, Peter Webb

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 ℤ.

Original languageEnglish (US)
Pages (from-to)1467-1481
Number of pages15
JournalAlgebras and Representation Theory
Issue number6
StatePublished - Dec 1 2017

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media Dordrecht.


  • Finitistic dimension
  • Gorenstein
  • Mackey functor


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