English

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.

Keywords

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