Hopf algebras are determined by their monoidal derived categories
Representation Theory
2025-02-25 v1 Category Theory
Rings and Algebras
Abstract
We show that two finite-dimensional Hopf algebras are gauge equivalent if and only if their bounded derived categories are monoidal triangulated equivalent. More generally, a monoidal derived equivalence between locally finite tensor Grothendieck categories induces a monoidal abelian equivalence.
Keywords
Cite
@article{arxiv.2502.16619,
title = {Hopf algebras are determined by their monoidal derived categories},
author = {Yuying Xu and Junhua Zheng},
journal= {arXiv preprint arXiv:2502.16619},
year = {2025}
}
Comments
18 pages. Any comments are welcome!