Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits
Abstract Following the recently obtained complete classification of quantum-deformed o $$ \mathfrak{o} $$ (4), o $$ \mathfrak{o} $$ (1, 3) and o $$ \mathfrak{o} $$ (2) algebras, characterized by classical r-matrices, we study their inhomogeneous D = 3 quantum IW contractions (i.e. the limit of vanis...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP09(2020)096 |
| _version_ | 1818478927108112384 |
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| author | Jerzy Kowalski-Glikman Jerzy Lukierski Tomasz Trześniewski |
| author_facet | Jerzy Kowalski-Glikman Jerzy Lukierski Tomasz Trześniewski |
| author_sort | Jerzy Kowalski-Glikman |
| collection | DOAJ |
| description | Abstract Following the recently obtained complete classification of quantum-deformed o $$ \mathfrak{o} $$ (4), o $$ \mathfrak{o} $$ (1, 3) and o $$ \mathfrak{o} $$ (2) algebras, characterized by classical r-matrices, we study their inhomogeneous D = 3 quantum IW contractions (i.e. the limit of vanishing cosmological constant), with Euclidean or Lorentzian signature. Subsequently, we compare our results with the complete list of D = 3 inhomogeneous Euclidean and D = 3 Poincaré quantum deformations obtained by P. Stachura. It turns out that the IW contractions allow us to recover all Stachura deformations. We further discuss the applicability of our results in the models of 3D quantum gravity in the Chern-Simons formulation (both with and with- out the cosmological constant), where it is known that the relevant quantum deformations should satisfy the Fock-Rosly conditions. The latter deformations in part of the cases are associated with the Drinfeld double structures, which also have been recently investigated in detail. |
| first_indexed | 2024-12-10T09:54:20Z |
| format | Article |
| id | doaj.art-85b6306402a144fba986fe15ce43e7dc |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-10T09:54:20Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-85b6306402a144fba986fe15ce43e7dc2022-12-22T01:53:33ZengSpringerOpenJournal of High Energy Physics1029-84792020-09-012020914210.1007/JHEP09(2020)096Quantum D = 3 Euclidean and Poincaré symmetries from contraction limitsJerzy Kowalski-Glikman0Jerzy Lukierski1Tomasz Trześniewski2Institute for Theoretical Physics, University of WrocławInstitute for Theoretical Physics, University of WrocławInstitute of Theoretical Physics, Jagiellonian UniversityAbstract Following the recently obtained complete classification of quantum-deformed o $$ \mathfrak{o} $$ (4), o $$ \mathfrak{o} $$ (1, 3) and o $$ \mathfrak{o} $$ (2) algebras, characterized by classical r-matrices, we study their inhomogeneous D = 3 quantum IW contractions (i.e. the limit of vanishing cosmological constant), with Euclidean or Lorentzian signature. Subsequently, we compare our results with the complete list of D = 3 inhomogeneous Euclidean and D = 3 Poincaré quantum deformations obtained by P. Stachura. It turns out that the IW contractions allow us to recover all Stachura deformations. We further discuss the applicability of our results in the models of 3D quantum gravity in the Chern-Simons formulation (both with and with- out the cosmological constant), where it is known that the relevant quantum deformations should satisfy the Fock-Rosly conditions. The latter deformations in part of the cases are associated with the Drinfeld double structures, which also have been recently investigated in detail.http://link.springer.com/article/10.1007/JHEP09(2020)096Models of Quantum GravityQuantum GroupsNon-Commutative Geometry |
| spellingShingle | Jerzy Kowalski-Glikman Jerzy Lukierski Tomasz Trześniewski Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits Journal of High Energy Physics Models of Quantum Gravity Quantum Groups Non-Commutative Geometry |
| title | Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits |
| title_full | Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits |
| title_fullStr | Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits |
| title_full_unstemmed | Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits |
| title_short | Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits |
| title_sort | quantum d 3 euclidean and poincare symmetries from contraction limits |
| topic | Models of Quantum Gravity Quantum Groups Non-Commutative Geometry |
| url | http://link.springer.com/article/10.1007/JHEP09(2020)096 |
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