Twisting Manin's universal quantum groups and comodule algebras

Huang H, Nguyen VC, Ure C, Vashaw KB, Veerapen P, Wang X. Twisting Manin's universal quantum groups and comodule algebras. Submitted.

Abstract

 Let $H$ be a Hopf algebra and $\sigma$ be a 2-cocycle on $H$. Using the tensor equivalence between the comodule categories of $H$ and of its 2-cocycle twist $H^\sigma$, we study twists of superpotentials, comodule algebras, and their associated universal quantum groups in the sense of Manin. In particular, we show the invariance of Artin--Schelter regularity of comodule algebras that are connected graded under a 2-cocycle twist of an infinite dimensional Hopf algebra. As a consequence, we show that Koszul AS-regular algebras of the same dimension and same Hilbert series are always 2-cocycle twists of each other, when viewed as comodule algebras over Manin's universal quantum groups.

Last updated on 09/26/2022