Generalized quantization scheme for central extensions of Lie algebras

TL;DR

This paper introduces a method for constructing nonlinear Poisson-Lie group structures on vector spaces and provides explicit quantization formulas for any central extension of Lie algebras.

Contribution

It offers a general quantization scheme applicable to all central extensions of Lie algebras, with explicit formulas.

Findings

Explicit quantization formulas for central extensions

Construction of nonlinear Poisson-Lie group structures

Applicable to arbitrary central extensions

Abstract

We present the method for finding of the nonlinear Poisson-Lie groups structures on the vector spaces and for their quantization. For arbitrary central extension of Lie algebra explicit formulas of quantization are proposed.