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arXiv · 2609.09525

Kleisli convolution representations and a Margolis--Sakurai version of the modular isomorphism problem

Yu-Zhe Liu
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Abstract

We introduce Kleisli convolution representations for groups, rings, and algebras. We show that their representation categories are equivalent to the usual ones for groups and finite-dimensional algebras, but for rings only recover modules whose underlying Abelian groups are free of finite rank. We also apply the Kleisli convolution representation to provide a partial answer to the Margolis--Sakurai version of the modular isomorphism problem.

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Yu-Zhe Liu. 2026-09-08. Kleisli convolution representations and a Margolis--Sakurai version of the modular isomorphism problem. https://arxiv.org/abs/2609.09525

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