Quantum groups – in particular, quantized universal enveloping algebras, or "QUEA’s" – over a symmetrizable Kac-Moody algebra were initially introduced as depending on just one “continuous” parameter, both in a "formal" and in a "polynomial" version. Later on, multiparameter QUEA’s have been introduced, with additional “discrete” parameters that affect only either the coalgebra structure or the algebra structure. In both cases, these multiparameter QUEA's can be realized as (Hopf) deformations – by twist or by 2-cocycle – of Drinfeld's celebrated QUEA, which is *uniparameter* instead.
In this talk I will introduce a newly minted family of (formal) multiparameter QUEA’s that encompasses and generalizes the previous ones: moreover, this family is also stable with respect to both deformations by twists and by 2-cocycles (of a special, "toral" type). Taking semiclassical limits, these new multiparameter QUEA’s give rise to a new family of multiparameter Lie bialgebras, that in turn is stable under both deformations by twists and by 2-cocycles (again of "toral" type), in the sense of Lie bialgebras.
All of this is a joint work with Gastón Andrés García, freely available as preprint arXiv:2203.11023 (2022).

A unifying approach to multiparameter quantum groups

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