Bicharacter twists of quantum groups

TL;DR

This paper introduces a method to generate two-parameter quantum groups from one-parameter versions using bicharacter twists, providing new proofs and generalizations for various quantum group presentations.

Contribution

It applies bicharacter twists to construct two-parameter quantum groups from standard one-parameter forms, offering new proofs and extending to super and multiparameter cases.

Findings

New elementary proofs of two-parameter quantum group results

Construction of two-parameter quantum groups via bicharacter twists

Generalizations to super and multiparameter quantum groups

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.