QUANTUM-SYMMETRIC EQUIVALENCE IS A GRADED MORITA INVARIANT

Document Type

Article

Publication Date

4-1-2025

Abstract

We show that if two m-homogeneous algebras have equivalent graded module categories, then they are quantum-symmetrically equivalent, that is, there is a monoidal equivalence between the categories of comodules for their associated universal quantum groups (in the sense of Manin) which sends one algebra to the other. As a consequence, any Zhang twist of an mhomogeneous algebra is a 2-cocycle twist by some 2-cocycle from its Manin’s universal quantum group.

Publication Source (Journal or Book title)

Proceedings of the American Mathematical Society

First Page

1389

Last Page

1409

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