Exponential Formulas and Lie Algebra Type Star Products
Given formal differential operators $F_i$ on polynomial algebrain 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 coprod...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2012-03-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2012.013 |
| _version_ | 1819154110125965312 |
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| author | Dragutin Svrtan Zoran Škoda Stjepan Meljanac Stjepan Meljanac Zoran Škoda Dragutin Svrtan |
| author_facet | Dragutin Svrtan Zoran Škoda Stjepan Meljanac Stjepan Meljanac Zoran Škoda Dragutin Svrtan |
| author_sort | Dragutin Svrtan |
| collection | DOAJ |
| description | Given formal differential operators $F_i$ on polynomial algebrain 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. |
| first_indexed | 2024-12-22T15:15:52Z |
| format | Article |
| id | doaj.art-591a27c4a3df44ae9940196e4da873d4 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-22T15:15:52Z |
| publishDate | 2012-03-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-591a27c4a3df44ae9940196e4da873d42022-12-21T18:21:45ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592012-03-018013Exponential Formulas and Lie Algebra Type Star ProductsDragutin SvrtanZoran ŠkodaStjepan MeljanacStjepan MeljanacZoran ŠkodaDragutin SvrtanGiven formal differential operators $F_i$ on polynomial algebrain 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.http://dx.doi.org/10.3842/SIGMA.2012.013star productexponential expressionformal differential operator |
| spellingShingle | Dragutin Svrtan Zoran Škoda Stjepan Meljanac Stjepan Meljanac Zoran Škoda Dragutin Svrtan Exponential Formulas and Lie Algebra Type Star Products Symmetry, Integrability and Geometry: Methods and Applications star product exponential expression formal differential operator |
| title | 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_short | Exponential Formulas and Lie Algebra Type Star Products |
| title_sort | exponential formulas and lie algebra type star products |
| topic | star product exponential expression formal differential operator |
| url | http://dx.doi.org/10.3842/SIGMA.2012.013 |
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