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SIGMA 8 (2012), 013, 15 pages arXiv:1006.0478
https://doi.org/10.3842/SIGMA.2012.013
Exponential Formulas and Lie Algebra Type Star Products
Stjepan Meljanac a, Zoran Škoda a and Dragutin Svrtan b
a) Division for Theoretical Physics, Institute Rudjer Bošković, Bijenička 54, P.O. Box 180, HR-10002 Zagreb, Croatia
b) Department of Mathematics, Faculty of Natural Sciences and Mathematics, University of Zagreb, HR-10000 Zagreb, Croatia
Received May 26, 2011, in final form March 01, 2012; Published online March 22, 2012
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.
Key words:
star product; exponential expression; formal differential operator.
pdf (439 kb)
tex (25 kb)
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