Twists of graded algebras in monoidal categories
Quantum Algebra
2024-08-13 v2 Category Theory
Rings and Algebras
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.
Cite
@article{arxiv.2311.18105,
title = {Twists of graded algebras in monoidal categories},
author = {Fernando Liu Lopez and Chelsea Walton},
journal= {arXiv preprint arXiv:2311.18105},
year = {2024}
}
Comments
v2: 34 pages. To appear in J. Algebra