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arXiv · 2508.10882

Bicharacter twists of quantum groups

Ian Martin·Alexander Tsymbaliuk
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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.

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Ian Martin, Alexander Tsymbaliuk. 2025-08-14. Bicharacter twists of quantum groups. https://arxiv.org/abs/2508.10882

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