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arXiv · 2311.18105

Twists of graded algebras in monoidal categories

Fernando Liu Lopez·Chelsea Walton
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Abstract

Zhang twists are a common tool for deforming graded algebras over a field in a way that preserves important ring-theoretic properties. We generalize Zhang twists to the setting of closed monoidal categories equipped with their self-enriched structure. Along the way, we prove several key results about algebraic structures in closed monoidal categories missing from the literature. We use these to ultimately prove Morita-type results, showcasing when graded algebras with equivalent categories of graded modules can be related by Zhang twists.

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BibTeXRIS

Fernando Liu Lopez, Chelsea Walton. 2023-11-29. Twists of graded algebras in monoidal categories. https://arxiv.org/abs/2311.18105

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