engleski

Exponential formulas and Lie algebra type star products

Given formal differential operators $F_i$ on polynomial algebra in several variables $x_1, …, x_n$, we discuss finding expressions $K_l$ determined by the equation $exp(∑_i x_i F_i)(exp(∑_j q_j x_j))=exp(∑_l K_l x_l)$ and their applications. The expressions for $K_l$ 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 $K_l$. We elaborate an example for a Lie algebra su(2), related to a quantum gravity application from the literature.

Weyl algebra; formal differential operator; exponential series; Lie algebra type star product

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