Quantum-symmetric equivalence via Manin's universal quantum groups

Abstract: We study 2-cocycle (and more generally quantum-symmetric equivalences between) twists of graded algebras via their associated universal quantum groups, in the sense of Manin. We prove that Zhang twists arise as a special case of 2-cocycle twist, and that 2-cocyle twisting preserves many fundamental homological invariants of graded algebras. As a consequence, we give a characterization of Artin--Schelter regular algebras using the language of 2-cocycle twists.

category theoryquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This online seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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