Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity
We present an in-depth investigation of the SL(2,R) momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and discuss their properties under Lorentz transformations. In particular we show...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2014 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146603 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity / M. Arzano, D. Latini, M. Lotito // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 33 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862575205218516992 |
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| author | Arzano, M. Latini, D. Lotito, M. |
| author_facet | Arzano, M. Latini, D. Lotito, M. |
| citation_txt | Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity / M. Arzano, D. Latini, M. Lotito // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 33 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present an in-depth investigation of the SL(2,R) momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and discuss their properties under Lorentz transformations. In particular we show how a certain set of coordinates exhibits an upper bound on the energy under deformed Lorentz boosts which saturate at the Planck energy. We discuss how this deformed symmetry framework is generally described by a quantum deformation of the Poincaré group: the quantum double of SL(2,R). We then illustrate how the space of functions on the group manifold momentum space has a dual representation on a non-commutative space of coordinates via a (quantum) group Fourier transform. In this context we explore the connection between Weyl maps and different notions of (quantum) group Fourier transform appeared in the literature in the past years and establish relations between them.
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| first_indexed | 2025-11-26T11:49:47Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146603 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T11:49:47Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Arzano, M. Latini, D. Lotito, M. 2019-02-10T09:53:00Z 2019-02-10T09:53:00Z 2014 Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity / M. Arzano, D. Latini, M. Lotito // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R50; 83A05; 83C99 DOI:10.3842/SIGMA.2014.079 https://nasplib.isofts.kiev.ua/handle/123456789/146603 We present an in-depth investigation of the SL(2,R) momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and discuss their properties under Lorentz transformations. In particular we show how a certain set of coordinates exhibits an upper bound on the energy under deformed Lorentz boosts which saturate at the Planck energy. We discuss how this deformed symmetry framework is generally described by a quantum deformation of the Poincaré group: the quantum double of SL(2,R). We then illustrate how the space of functions on the group manifold momentum space has a dual representation on a non-commutative space of coordinates via a (quantum) group Fourier transform. In this context we explore the connection between Weyl maps and different notions of (quantum) group Fourier transform appeared in the literature in the past years and establish relations between them. This paper is a contribution to the Special Issue on Deformations of Space-Time and its Symmetries. The
 full collection is available at http://www.emis.de/journals/SIGMA/space-time.html. 
 We would like to thank the anonymous referees for the insightful comments which helped us
 improve the paper. MA work is supported by a Marie Curie Career Integration Grant within
 the 7th European Community Framework Programme and in part by a grant from the John
 Templeton Foundation. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity Article published earlier |
| spellingShingle | Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity Arzano, M. Latini, D. Lotito, M. |
| title | Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity |
| title_full | Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity |
| title_fullStr | Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity |
| title_full_unstemmed | Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity |
| title_short | Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity |
| title_sort | group momentum space and hopf algebra symmetries of point particles coupled to 2+1 gravity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146603 |
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