Heisenberg Doubles for Snyder-Type Models
A Snyder model generated by the noncommutative coordinates and Lorentz generators closes a Lie algebra. The application of the Heisenberg double construction is investigated for the Snyder coordinates and momenta generators. This leads to the phase space of the Snyder model. Further, the extended Sn...
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| Format: | Article |
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MDPI AG
2021-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/6/1055 |
| _version_ | 1797530453063761920 |
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| author | Stjepan Meljanac Anna Pachoł |
| author_facet | Stjepan Meljanac Anna Pachoł |
| author_sort | Stjepan Meljanac |
| collection | DOAJ |
| description | A Snyder model generated by the noncommutative coordinates and Lorentz generators closes a Lie algebra. The application of the Heisenberg double construction is investigated for the Snyder coordinates and momenta generators. This leads to the phase space of the Snyder model. Further, the extended Snyder algebra is constructed by using the Lorentz algebra, in one dimension higher. The dual pair of extended Snyder algebra and extended Snyder group is then formulated. Two Heisenberg doubles are considered, one with the conjugate tensorial momenta and another with the Lorentz matrices. Explicit formulae for all Heisenberg doubles are given. |
| first_indexed | 2024-03-10T10:30:12Z |
| format | Article |
| id | doaj.art-5274a6183a3e4a82a98b96dffcf46d06 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T10:30:12Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-5274a6183a3e4a82a98b96dffcf46d062023-11-21T23:44:14ZengMDPI AGSymmetry2073-89942021-06-01136105510.3390/sym13061055Heisenberg Doubles for Snyder-Type ModelsStjepan Meljanac0Anna Pachoł1Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička c.54, 10002 Zagreb, CroatiaFaculty of Science and Engineering, Queen Mary University of London, Mile End Rd., London E1 4NS, UKA Snyder model generated by the noncommutative coordinates and Lorentz generators closes a Lie algebra. The application of the Heisenberg double construction is investigated for the Snyder coordinates and momenta generators. This leads to the phase space of the Snyder model. Further, the extended Snyder algebra is constructed by using the Lorentz algebra, in one dimension higher. The dual pair of extended Snyder algebra and extended Snyder group is then formulated. Two Heisenberg doubles are considered, one with the conjugate tensorial momenta and another with the Lorentz matrices. Explicit formulae for all Heisenberg doubles are given.https://www.mdpi.com/2073-8994/13/6/1055quantum groupsHeisenberg doublesSnyder model |
| spellingShingle | Stjepan Meljanac Anna Pachoł Heisenberg Doubles for Snyder-Type Models Symmetry quantum groups Heisenberg doubles Snyder model |
| title | Heisenberg Doubles for Snyder-Type Models |
| title_full | Heisenberg Doubles for Snyder-Type Models |
| title_fullStr | Heisenberg Doubles for Snyder-Type Models |
| title_full_unstemmed | Heisenberg Doubles for Snyder-Type Models |
| title_short | Heisenberg Doubles for Snyder-Type Models |
| title_sort | heisenberg doubles for snyder type models |
| topic | quantum groups Heisenberg doubles Snyder model |
| url | https://www.mdpi.com/2073-8994/13/6/1055 |
| work_keys_str_mv | AT stjepanmeljanac heisenbergdoublesforsnydertypemodels AT annapachoł heisenbergdoublesforsnydertypemodels |