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SIGMA, 2012, Volume 8, 013, 15 pages (Mi sigma690)  

This article is cited in 10 scientific papers (total in 10 papers)

Exponential formulas and Lie algebra type star products

Stjepan Meljanaca, Zoran Škodaa, Dragutin Svrtanb

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

Abstract: 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 $\exp(\sum_i x_i F_i)(\exp(\sum_j q_j x_j)) = \exp(\sum_l K_l x_l)$ 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.

DOI: https://doi.org/10.3842/SIGMA.2012.013

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Full text: http://emis.mi.ras.ru/.../013
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Bibliographic databases:

ArXiv: 1006.0478
MSC: 81R60; 16S30; 16S32; 16A58
Received: May 26, 2011; in final form March 1, 2012; Published online March 22, 2012
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Citation: Stjepan Meljanac, Zoran Škoda, Dragutin Svrtan, “Exponential formulas and Lie algebra type star products”, SIGMA, 8 (2012), 013, 15 pp.

Citation in format AMSBIB
\Bibitem{MelKodSvr12}
\by Stjepan Meljanac, Zoran {\v S}koda, Dragutin Svrtan
\paper Exponential formulas and Lie algebra type star products
\jour SIGMA
\yr 2012
\vol 8
\papernumber 013
\totalpages 15
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\crossref{https://doi.org/10.3842/SIGMA.2012.013}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84858966959}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Michele Arzano, Danilo Latini, Matteo Lotito, “Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to $\boldsymbol{2+1}$ Gravity”, SIGMA, 10 (2014), 079, 23 pp.  mathnet  crossref
    2. D. Kovacevic, S. Meljanac, A. Samsarov, Z. Skoda, “Hermitian realizations of $\kappa$-Minkowski space-time”, Int. J. Mod. Phys. A, 30:3, SI (2015), 1550019  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. T. Juric, S. Meljanac, D. Pikutic, “Realizations of $\kappa$-Minkowski space, drinfeld twists, and related symmetry algebras”, Eur. Phys. J. C, 75:11 (2015), 528  crossref  adsnasa  isi  scopus
    4. M. Khodadi, K. Nozari, “Some features of scattering problem in a $\kappa$-deformed Minkowski spacetime”, Ann. Phys.-Berlin, 528:11-12 (2016), 785–795  crossref  isi  scopus
    5. S. Meljanac, S. Kresic-Juric, T. Martinic, “The Weyl realizations of Lie algebras, and left-right duality”, J. Math. Phys., 57:5 (2016), 051704  crossref  mathscinet  zmath  isi  elib  scopus
    6. S. Meljanac, D. Meljanac, F. Mercati, D. Pikutic, “Noncommutative spaces and Poincaré symmetry”, Phys. Lett. B, 766 (2017), 181–185  crossref  isi  scopus
    7. S. Meljanac, D. Meljanac, S. Mignemi, R. Strajn, “Snyder-type space times, twisted Poincaré algebra and addition of momenta”, Int. J. Mod. Phys. A, 32:28-29 (2017), 1750172  crossref  mathscinet  zmath  isi  scopus
    8. S. Meljanac, D. Meljanac, A. Pachol, D. Pikutic, “Remarks on simple interpolation between Jordanian twists”, J. Phys. A-Math. Theor., 50:26 (2017), 265201  crossref  mathscinet  zmath  isi  scopus
    9. S. Meljanac, D. Meljanac, S. Mignemi, R. Strajn, “Quantum field theory in generalised Snyder spaces”, Phys. Lett. B, 768 (2017), 321–325  crossref  zmath  isi  scopus
    10. Stjepan Meljanac, Zoran Škoda, “Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures”, SIGMA, 14 (2018), 026, 23 pp.  mathnet  crossref
  • Symmetry, Integrability and Geometry: Methods and Applications
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