an:06050751
Zbl 1248.81092
Meljanac, Stjepan; ??koda, Zoran; Svrtan, Dragutin
Exponential formulas and Lie algebra type star products
EN
SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 013, 15 p. (2012).
00302161
2012
j
81R60 16S30 16S32 83C45 83C65
star product; exponential expression; formal differential operator
Summary: Given formal differential operators \(F_i\) on polynomial algebra in several variables \(x_1,\ldots,x_n\), we discuss finding expressions \(K_l\) determined by the equation \(\exp(\sum_i x_i F_i)(\exp(\sum_j q_j x_j)) = \exp(\sum_l K_l x_l)\) 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.