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SIGMA, 2014, Volume 10, 107, 24 pages (Mi sigma972)  

This article is cited in 15 scientific papers (total in 15 papers)

$\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes

Andrzej Borowieca, Anna Pachołbc

a Institute for Theoretical Physics, pl. M. Borna 9, 50-204 Wrocław, Poland
b Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik, Iceland
c Capstone Institute for Theoretical Research, Reykjavik, Iceland

Abstract: We extend our previous study of Hopf-algebraic $\kappa$-deformations of all inhomogeneous orthogonal Lie algebras $\mathrm{iso}(g)$ as written in a tensorial and unified form. Such deformations are determined by a vector $\tau$ 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 $\kappa$-Minkowski (Hopf) module algebras. Secondly, $h$-adic vs $q$-analog (polynomial) versions of deformed algebras including specialization of the formal deformation parameter $\kappa$ 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 $\kappa$-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.

Keywords: quantum deformations; quantum groups; quantum spaces; reality condition for Hopf module algebras; $q$-analog and specialization versions; $\kappa$-Minkowski spacetime; extended $\kappa$-deformations; twist-deformations; classification of solvable Lie algebras.

DOI: https://doi.org/10.3842/SIGMA.2014.107

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ArXiv: 1404.2916
MSC: 81T75; 58B22; 16T05; 17B37; 81R60
Received: April 11, 2014; in final form November 11, 2014; Published online November 22, 2014
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Citation: Andrzej Borowiec, Anna Pachoł, “$\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes”, SIGMA, 10 (2014), 107, 24 pp.

Citation in format AMSBIB
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\by Andrzej~Borowiec, Anna~Pacho\l
\paper $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
\jour SIGMA
\yr 2014
\vol 10
\papernumber 107
\totalpages 24
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\crossref{https://doi.org/10.3842/SIGMA.2014.107}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ballesteros A. Herranz F.J. Naranjo P., “Towards (3+1) Gravity Through Drinfel'D Doubles With Cosmological Constant”, Phys. Lett. B, 746 (2015), 37–43  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Borowiec A., Juric T., Meljanac S., Pachol A., “Central tetrads and quantum spacetimes”, Int. J. Geom. Methods Mod. Phys., 13:8, SI (2016), 1640005  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. Borowiec, A. Pachol, “Twisted bialgebroids versus bialgebroids from a Drinfeld twist”, J. Phys. A-Math. Theor., 50:5 (2017), 055205  crossref  mathscinet  zmath  isi  scopus
    4. Kh. P. Gnatenko, V. M. Tkachuk, “Many-particle system in a rotationally-invariant space with canonical noncommutativity of coordinates”, J. Phys. Stud., 21:4 (2017), 4002  mathscinet  isi
    5. Kh. P. Gnatenko, V. M. Tkachuk, “Noncommutative phase space with rotational symmetry and hydrogen atom”, Int. J. Mod. Phys. A, 32:26 (2017), 1750161  crossref  mathscinet  zmath  isi
    6. P. Aschieri, A. Borowiec, A. Pachol, “Observables and dispersion relations in kappa-Minkowski spacetime”, J. High Energy Phys., 2017, no. 10, 152  crossref  mathscinet  zmath  isi  scopus
    7. N. Beisert, R. Hecht, B. Hoare, “Maximally extended ${\mathfrak{sl}}(2|2)$, $q$-deformed $\mathfrak d(2,1;\epsilon)$ and $\mathrm{3D}$ kappa-Poincaré”, J. Phys. A-Math. Theor., 50:31 (2017), 314003  crossref  mathscinet  zmath  isi  scopus
    8. Kh. P. Gnatenko, V O. Shyiko, “Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space”, Mod. Phys. Lett. A, 33:16 (2018), 1850091  crossref  mathscinet  zmath  isi  scopus
    9. Kh. P. Gnatenko, O. O. Morozko, Yu. S. Krynytskyi, “The motion of a particle in a gravitational field in a rotationally-invariant noncommutative space of a canonical type and the weak equivalence principle”, J. Phys. Stud., 22:1 (2018), 1001  crossref  mathscinet  isi
    10. Kh. P. Gnatenko, “Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle”, EPL, 123:5 (2018), 50002  crossref  isi  scopus
    11. Kh. P. Gnatenko, “System of interacting harmonic oscillators in rotationally invariant noncommutative phase space”, Phys. Lett. A, 382:46 (2018), 3317–3324  crossref  mathscinet  isi  scopus
    12. Kuznetsova Zh., Toppan F., “On Light-Like Deformations of the Poincare Algebra”, Eur. Phys. J. C, 79:1 (2019), 27  crossref  isi  scopus
    13. Gnatenko Kh.P., Samar I M., Tkachuk V.M., “Time-Reversal and Rotational Symmetries in Noncommutative Phase Space”, Phys. Rev. A, 99:1 (2019), 012114  crossref  mathscinet  isi  scopus
    14. Borowiec A., Brocki L., Kowalski-Glikman J., Unger J., “Kappa-Deformed Bms Symmetry”, Phys. Lett. B, 790 (2019), 415–420  crossref  mathscinet  zmath  isi  scopus
    15. Gnatenko Kh.P., “Harmonic Oscillator Chain in Noncommutative Phase Space With Rotational Symmetry”, Ukr. J. Phys., 64:2 (2019), 131–136  crossref  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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