English

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!

R2 v1 2026-07-01T04:50:24.466Z