κ-Deformed Phase Space, Hopf Algebroid and Twisting
Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to obtain an algebra structure. We use the dual base to construct the target map and antipode. The notion o...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2014 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2014
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146538 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | κ-Deformed Phase Space, Hopf Algebroid and Twisting / T. Jurić, D. Kovačević, S. Meljanac // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 65 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862564513294843904 |
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| author | Jurić, T. Kovačević, D. Meljanac, S. |
| author_facet | Jurić, T. Kovačević, D. Meljanac, S. |
| citation_txt | κ-Deformed Phase Space, Hopf Algebroid and Twisting / T. Jurić, D. Kovačević, S. Meljanac // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 65 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to obtain an algebra structure. We use the dual base to construct the target map and antipode. The notion of twist is analyzed for κ-deformed phase space in Hopf algebroid setting. It is outlined how the twist in the Hopf algebroid setting reproduces the full Hopf algebra structure of κ-Poincaré algebra. Several examples of realizations are worked out in details.
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| first_indexed | 2025-11-25T23:46:46Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146538 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T23:46:46Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Jurić, T. Kovačević, D. Meljanac, S. 2019-02-09T20:58:50Z 2019-02-09T20:58:50Z 2014 κ-Deformed Phase Space, Hopf Algebroid and Twisting / T. Jurić, D. Kovačević, S. Meljanac // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 65 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R60; 17B37; 81R50 DOI:10.3842/SIGMA.2014.106 https://nasplib.isofts.kiev.ua/handle/123456789/146538 Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to obtain an algebra structure. We use the dual base to construct the target map and antipode. The notion of twist is analyzed for κ-deformed phase space in Hopf algebroid setting. It is outlined how the twist in the Hopf algebroid setting reproduces the full Hopf algebra structure of κ-Poincaré algebra. Several examples of realizations are worked out in details. 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.
 The authors would like to thank A. Borowiec, J. Lukierski, A. Pachol, R. Strajn and Z. ˇ Skoda for ˇ
 useful discussions and comments. The authors would also like to thank the anonymous referee
 for useful comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications κ-Deformed Phase Space, Hopf Algebroid and Twisting Article published earlier |
| spellingShingle | κ-Deformed Phase Space, Hopf Algebroid and Twisting Jurić, T. Kovačević, D. Meljanac, S. |
| title | κ-Deformed Phase Space, Hopf Algebroid and Twisting |
| title_full | κ-Deformed Phase Space, Hopf Algebroid and Twisting |
| title_fullStr | κ-Deformed Phase Space, Hopf Algebroid and Twisting |
| title_full_unstemmed | κ-Deformed Phase Space, Hopf Algebroid and Twisting |
| title_short | κ-Deformed Phase Space, Hopf Algebroid and Twisting |
| title_sort | κ-deformed phase space, hopf algebroid and twisting |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146538 |
| work_keys_str_mv | AT jurict κdeformedphasespacehopfalgebroidandtwisting AT kovacevicd κdeformedphasespacehopfalgebroidandtwisting AT meljanacs κdeformedphasespacehopfalgebroidandtwisting |