Abstract:Let $G$ be a finite group. We provide a description of the ordinary quiver of the complex monoid algebra of the wreath product $G \wr \mathrm{PT}_n$, where $\mathrm{PT}_n$ denotes the monoid of all partial functions on an $n$-element set. This description depends on the multiplicities of simple $G$-modules appearing in the decomposition of tensor products of simple $G$-modules. We also prove that the global dimension of this algebra is $n-1$. Both results are obtained by analyzing the associated Ehresmann EI-category related to the monoid. Finally, we describe the quiver of the algebra of the wreath product of $G$ with the submonoid of all order-preserving partial functions.
From: Itamar Stein [view email]
[v1]
Wed, 24 Jun 2026 10:43:22 UTC (41 KB)
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