Document Type

Article

Publication Date

5-1-2024

Abstract

We introduce the notion of quantum-symmetric equivalence of two connected graded algebras, based on Morita–Takeuchi equivalences of their universal quantum groups, in the sense of Manin. We study homological and algebraic invariants of quantum-symmetric equivalence classes, and prove that numerical Tor-regularity, Castelnuovo–Mumford regularity, Artin–Schelter regularity, and the Frobenius property are invariant under any Morita–Takeuchi equivalence. In particular, by combining our results with the work of Raedschelders and Van den Bergh, we prove that Koszul Artin–Schelter regular algebras of a fixed global dimension form a single quantum-symmetric equivalence class. Moreover, we characterize 2-cocycle twists (which arise as a special case of quantum-symmetric equivalence) of Koszul duals, of superpotentials, of superpotential algebras, of Nakayama automorphisms of twisted Frobenius algebras, and of Artin–Schelter regular algebras. We also show that finite generation of Hochschild cohomology rings is preserved under certain 2-cocycle twists.

Publication Source (Journal or Book title)

Advances in Mathematics

Download

Share

COinS