Work

Quantum-symmetric equivalence is a graded Morita invariant

Year: 2025

Type: article

Abstract: We show that if two m 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 m m -homogeneous algebra is a 2-cocycle twist by some 2-cocycle from its Manin’s universal quantum group.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17113

Authors: Hongdi Huang, Van Nguyen, Kent Vashaw, Padmini Veerapen, Xingting Wang

Institutions: Shanghai University, United States Naval Academy, University of California, Los Angeles, Tennessee Technological University, Louisiana State University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: PostDoctoral Research Fellowship, RUI: Homological Techniques in Quantum Symmetries