Bicharacter twists of quantum groups
Representation Theory
2025-08-15 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
We apply the general construction of a twist of bigraded Hopf algebras by skew bicharacters to obtain two-parameter quantum groups in the Drinfeld-Jimbo, new Drinfeld (for affine types), and FRT (for both finite and affine) presentations from their standard one-parameter versions. This yields new elementary proofs of the fundamental results on two-parameter quantum groups that appeared in the literature over the last two decades, and also leads to natural generalizations in the super and multiparameter cases.
Keywords
Cite
@article{arxiv.2508.10882,
title = {Bicharacter twists of quantum groups},
author = {Ian Martin and Alexander Tsymbaliuk},
journal= {arXiv preprint arXiv:2508.10882},
year = {2025}
}
Comments
v1: 72pp, comments are welcome!