Exponential Formulas and Lie Algebra Type Star Products

Abstract

Given formal differential operators Fi on polynomial algebra in several variables x₁,…,xn, we discuss finding expressions Kl determined by the equation exp(∑ixiFi)(exp(∑jqjxj))=exp(∑lKlxl) and their applications. The expressions for Kl are related to the coproducts for deformed momenta for the noncommutative space-times of Lie algebra type and also appear in the computations with a class of star products. We find combinatorial recursions and derive formal differential equations for finding Kl. We elaborate an example for a Lie algebra su(2), related to a quantum gravity application from the literature.