Exponential Formulas and Lie Algebra Type Star Products
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 nonco...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148390 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Exponential Formulas and Lie Algebra Type Star Products / S. Meljanac, Z. Škoda, D. Svrtan // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 22 назв. — англ. |
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Meljanac, S. Škoda, Z. Svrtan, D. 2019-02-18T11:25:52Z 2019-02-18T11:25:52Z 2012 Exponential Formulas and Lie Algebra Type Star Products / S. Meljanac, Z. Škoda, D. Svrtan // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R60; 16S30; 16S32; 16A58 DOI: http://dx.doi.org/10.3842/SIGMA.2012.013 https://nasplib.isofts.kiev.ua/handle/123456789/148390 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. We thank the Croatia MSES projects for partial supports: 098-0000000-2865 (S.M. and Z.S.), 037-0372794-2807 (Z.S.) and 037-0000000-2779 (D.S.). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Exponential Formulas and Lie Algebra Type Star Products Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Exponential Formulas and Lie Algebra Type Star Products |
| spellingShingle |
Exponential Formulas and Lie Algebra Type Star Products Meljanac, S. Škoda, Z. Svrtan, D. |
| title_short |
Exponential Formulas and Lie Algebra Type Star Products |
| title_full |
Exponential Formulas and Lie Algebra Type Star Products |
| title_fullStr |
Exponential Formulas and Lie Algebra Type Star Products |
| title_full_unstemmed |
Exponential Formulas and Lie Algebra Type Star Products |
| title_sort |
exponential formulas and lie algebra type star products |
| author |
Meljanac, S. Škoda, Z. Svrtan, D. |
| author_facet |
Meljanac, S. Škoda, Z. Svrtan, D. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148390 |
| citation_txt |
Exponential Formulas and Lie Algebra Type Star Products / S. Meljanac, Z. Škoda, D. Svrtan // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 22 назв. — англ. |
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AT meljanacs exponentialformulasandliealgebratypestarproducts AT skodaz exponentialformulasandliealgebratypestarproducts AT svrtand exponentialformulasandliealgebratypestarproducts |
| first_indexed |
2025-12-07T17:49:48Z |
| last_indexed |
2025-12-07T17:49:48Z |
| _version_ |
1850872732772728832 |