Exponential Formulas and Lie Algebra Type Star Products
Stjepan Meljanac, Zoran \v{S}koda, Dragutin Svrtan

TL;DR
This paper develops formulas and recursive methods to compute exponential expressions involving differential operators, with applications to noncommutative geometry and quantum gravity.
Contribution
It introduces new recursive formulas and differential equations for calculating exponential operator expressions related to Lie algebra star products.
Findings
Derived combinatorial recursions for $K_l$
Established differential equations for exponential expressions
Applied methods to $su(2)$ Lie algebra example
Abstract
Given formal differential operators on polynomial algebra in several variables , we discuss finding expressions determined by the equation and their applications. The expressions for 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 . We elaborate an example for a Lie algebra , related to a quantum gravity application from the literature.
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