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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| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146537 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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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irk-123456789-1465372019-02-11T01:23:40Z κ-Deformations and extended κ-Minkowski spacetimes Borowiec, A. Pachoł, A. 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. 2014 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146537 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Borowiec, A. Pachoł, A. |
| spellingShingle |
Borowiec, A. Pachoł, A. κ-Deformations and extended κ-Minkowski spacetimes Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Borowiec, A. Pachoł, A. |
| author_sort |
Borowiec, A. |
| title |
κ-Deformations and extended κ-Minkowski spacetimes |
| title_short |
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_sort |
κ-deformations and extended κ-minkowski spacetimes |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146537 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT borowieca kdeformationsandextendedkminkowskispacetimes AT pachoła kdeformationsandextendedkminkowskispacetimes |
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2025-07-11T00:12:21Z |
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2025-07-11T00:12:21Z |
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