κ-Deformations and extended κ-Minkowski spacetimes
We extend our previous study of Hopf-algebraic κ-deformations of all inhomogeneous orthogonal Lie algebras iso(g) as written in a tensorial and unified form. Such deformations are determined by a vector τ which for Lorentzian signature can be taken time-, light- or space-like. We focus on some mathe...
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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/123456789/146537 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | κ-Deformations and extended κ-Minkowski spacetimes/ A. Borowiec, A. Pachoł // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 88 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862602254080540672 |
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| author | Borowiec, A. Pachoł, A. |
| author_facet | Borowiec, A. Pachoł, A. |
| citation_txt | κ-Deformations and extended κ-Minkowski spacetimes/ A. Borowiec, A. Pachoł // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 88 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We extend our previous study of Hopf-algebraic κ-deformations of all inhomogeneous orthogonal Lie algebras iso(g) as written in a tensorial and unified form. Such deformations are determined by a vector τ which for Lorentzian signature can be taken time-, light- or space-like. We focus on some mathematical aspects related to this subject. Firstly, we describe real forms with connection to the metric's signatures and their compatibility with the reality condition for the corresponding κ-Minkowski (Hopf) module algebras. Secondly, h-adic vs q-analog (polynomial) versions of deformed algebras including specialization of the formal deformation parameter κ to some numerical value are considered. In the latter the general covariance is lost and one deals with an orthogonal decomposition. The last topic treated in this paper concerns twisted extensions of κ-deformations as well as the description of resulting noncommutative spacetime algebras in terms of solvable Lie algebras. We found that if the type of the algebra does not depend on deformation parameters then specialization is possible.
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| first_indexed | 2025-11-28T02:24:45Z |
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| id | nasplib_isofts_kiev_ua-123456789-146537 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-28T02:24:45Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
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| spelling | Borowiec, A. Pachoł, A. 2019-02-09T20:43:50Z 2019-02-09T20:43:50Z 2014 κ-Deformations and extended κ-Minkowski spacetimes/ A. Borowiec, A. Pachoł // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 88 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81T75; 58B22; 16T05; 17B37; 81R60 DOI:10.3842/SIGMA.2014.107 https://nasplib.isofts.kiev.ua/handle/123456789/146537 We extend our previous study of Hopf-algebraic κ-deformations of all inhomogeneous orthogonal Lie algebras iso(g) as written in a tensorial and unified form. Such deformations are determined by a vector τ which for Lorentzian signature can be taken time-, light- or space-like. We focus on some mathematical aspects related to this subject. Firstly, we describe real forms with connection to the metric's signatures and their compatibility with the reality condition for the corresponding κ-Minkowski (Hopf) module algebras. Secondly, h-adic vs q-analog (polynomial) versions of deformed algebras including specialization of the formal deformation parameter κ to some numerical value are considered. In the latter the general covariance is lost and one deals with an orthogonal decomposition. The last topic treated in this paper concerns twisted extensions of κ-deformations as well as the description of resulting noncommutative spacetime algebras in terms of solvable Lie algebras. We found that if the type of the algebra does not depend on deformation parameters then specialization is possible. 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 are grateful to V. Lyakhovsky for collaboration and discussions during the early stages of the
 work presented in Section 4. We are also indebted to J. Lukierski for critical remarks and pointing
 out the reference [60]. We would like to thank to the anonymous referees for relevant suggestions
 to improve the paper. This work is a part of the Polish National Science Centre (NCN) project
 2011/01/B/ST2/03354. AB acknowledges the financial support from FSS Mobility and Training
 Program as well as the hospitality of the Science Institute of University of Iceland. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications κ-Deformations and extended κ-Minkowski spacetimes Article published earlier |
| spellingShingle | κ-Deformations and extended κ-Minkowski spacetimes Borowiec, A. Pachoł, A. |
| title | κ-Deformations and extended κ-Minkowski spacetimes |
| title_full | κ-Deformations and extended κ-Minkowski spacetimes |
| title_fullStr | κ-Deformations and extended κ-Minkowski spacetimes |
| title_full_unstemmed | κ-Deformations and extended κ-Minkowski spacetimes |
| title_short | κ-Deformations and extended κ-Minkowski spacetimes |
| title_sort | κ-deformations and extended κ-minkowski spacetimes |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146537 |
| work_keys_str_mv | AT borowieca κdeformationsandextendedκminkowskispacetimes AT pachoła κdeformationsandextendedκminkowskispacetimes |