Mackey algebras which are Gorenstein
Ivo Dell'Ambrogio, Jan \v{S}\v{t}ov\'i\v{c}ek
TL;DR
This paper characterizes when the integral Mackey algebra is Gorenstein, showing it occurs if and only if the group order is square-free, with Gorenstein dimension one, supported by specific group examples.
Contribution
It provides a complete characterization of the Gorenstein property for integral Mackey algebras based on the group's order, filling a gap in the literature.
Findings
Integral Mackey algebra is Gorenstein iff group order is square-free.
Gorenstein dimension of such algebras is one.
Detailed analysis of cyclic group of order four and Klein four group.
Abstract
We complete the picture available in the literature by showing that the integral Mackey algebra is Gorenstein if and only if the group order is square-free, in which case it must have Gorenstein dimension one. We illustrate this result by looking in details at the examples of the cyclic group of order four and the Klein four group.
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