Bicharacter twists of quantum groups

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.

Publication Details

Journal
ArXiv.org
Published
2025-08-14
Primary Topic
Algebraic structures and combinatorial models
Type
article
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article

Bicharacter twists of quantum groups

ArXiv.org
Algebraic structures and combinatorial models
article

Bicharacter twists of quantum groups

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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.

ArXiv.org
Openalex Percentile: Top 44%
Algebraic structures and combinatorial models
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Bicharacter twists of quantum groups · ArXiv.org (2025) | TGRS Research Map | TGRS