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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2012 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2012
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148390 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862714270849957888 |
|---|---|
| author | Meljanac, S. Škoda, Z. Svrtan, D. |
| author_facet | Meljanac, S. Škoda, Z. Svrtan, D. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T17:49:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148390 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:49:48Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Exponential Formulas and Lie Algebra Type Star Products Meljanac, S. Škoda, Z. Svrtan, D. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148390 |
| work_keys_str_mv | AT meljanacs exponentialformulasandliealgebratypestarproducts AT skodaz exponentialformulasandliealgebratypestarproducts AT svrtand exponentialformulasandliealgebratypestarproducts |