Quantization of Gamma-Lie bialgebras

TL;DR

This paper introduces Gamma-Lie bialgebras, expanding the class of co-Poisson algebras that can be quantized, and studies their behavior under twist compositions.

Contribution

It defines Gamma-Lie bialgebras and constructs their quantization functors, extending known quantization results to a broader class of co-Poisson algebras.

Findings

Construction of quantization functors for Gamma-Lie bialgebras

Extension of quantization methods to cocommutative co-Poisson algebras

Analysis of quantization behavior under twist compositions

Abstract

We introduce the notion of Gamma-Lie bialgebra, where Gamma is a group. These objects give rise to cocommutative co-Poisson algebras, for which we construct quantization functors. This enlarges the class of co-Poisson algebras for which a quantization is known. Our result relies on our earlier work, where we showed that twists of Lie bialgebras can be quantized; we complement this work by studying the behavior of this quantization under compositions of twists.