We consider 2-cocycle twists (and more generally, Morita-Takeuchi equivalences between) Manin’s universal quantum groups and their comodule algebras. We show when Zhang twists of connected graded algebras can be realized as cocycle twists, thus concretely connected the (graded) representation theory of an algebra A to the corepresentation theory of its universal quantum group. We also prove that fundamental properties of non-commutative associative algebras, such as Artin-Schelter regularity and Koszuality are preserved under 2-cocycle twist.
This is joint work with Hongdi Huang, Van Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang.
This video was part of the Maurice Auslander International Conference.
