The Galois Alperin weight conjecture for finite category algebras
Xin Huang

TL;DR
This paper formulates a Galois Alperin weight conjecture for finite category algebras, reducing it to the case of finite groups, and extends it to EI-categories with a blockwise version.
Contribution
It introduces a new conjecture for finite category algebras, linking simple modules and weights, and reduces the problem to finite groups, extending to EI-categories.
Findings
Formulated a Galois Alperin weight conjecture for finite category algebras.
Reduced the conjecture to the case of finite groups.
Extended the conjecture to EI-categories with a blockwise formulation.
Abstract
Let be a prime, an algebraic closure of and the Galois group . Let be a finite category and the -orbit category of defined by Linckelmann. We formulate a version of the Galois Alperin weight conjecture (GAWC) for finite category algebras stating that there exists a -equivariant bijection between the set of isomorphism classes of simple -modules and that of the weights of . We reduce the GAWC for finite categories to finite groups. For an EI-category, we give a partition of weights of with respect to blocks of and then formulate a blockwise Galois Alperin weight conjecture (BGAWC) for . Similarly, we reduce the BGAWC for…
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