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Exponential formulas and Lie algebra type star products
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012) Cet article a éte moissonné depuis la source Math-Net.Ru

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Given formal differential operators $F_i$ on polynomial algebra in several variables $x_1,\dots,x_n$, 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.
Keywords: star product, exponential expression, formal differential operator. 
@article{SIGMA_2012_8_a12,
     author = {Stjepan Meljanac and Zoran \v{S}koda and Dragutin Svrtan},
     title = {Exponential formulas and {Lie} algebra type star products},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2012},
     volume = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a12/}
}
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Stjepan Meljanac; Zoran Škoda; Dragutin Svrtan. Exponential formulas and Lie algebra type star products. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a12/

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