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SIGMA, 2014, Volume 10, 106, 18 pages (Mi sigma971)  

This article is cited in 20 scientific papers (total in 20 papers)

$\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting

Tajron Jurića, Domagoj Kovačevićb, Stjepan Meljanaca

a Rudjer Bošković Institute, Bijenička cesta 54, HR-10000 Zagreb, Croatia
b Faculty of Electrical Engineering and Computing, Unska 3, HR-10000 Zagreb, Croatia

Abstract: 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 $\kappa$-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 $\kappa$-Poincaré algebra. Several examples of realizations are worked out in details.

Keywords: noncommutative space; $\kappa$-Minkowski spacetime; Hopf algebroid; $\kappa$-Poincaré algebra; realizations; twist.


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ArXiv: 1402.0397
MSC: 81R60; 17B37; 81R50
Received: February 21, 2014; in final form November 11, 2014; Published online November 18, 2014

Citation: Tajron Jurić, Domagoj Kovačević, Stjepan Meljanac, “$\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting”, SIGMA, 10 (2014), 106, 18 pp.

Citation in format AMSBIB
\by Tajron~Juri\'c, Domagoj~Kova{\v{c}}evi\'c, Stjepan~Meljanac
\paper $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
\jour SIGMA
\yr 2014
\vol 10
\papernumber 106
\totalpages 18

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    This publication is cited in the following articles:
    1. Lukierski J. Skoda Z. Woronowicz M., “Kappa-Deformed Covariant Quantum Phase Spaces as Hopf Algebroids”, Phys. Lett. B, 750 (2015), 401–406  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Juric T., Meljanac S., Pikutic D., “Realizations of Kappa-Minkowski Space, Drinfeld Twists, and Related Symmetry Algebras”, Eur. Phys. J. C, 75:11 (2015), 528  crossref  adsnasa  isi  scopus
    3. Juric T., Meljanac S., Pikutic D., Strajn R., “Toward the Classification of Differential Calculi on Kappa-Minkowski Space and Related Field Theories”, J. High Energy Phys., 2015, no. 7, 055  crossref  mathscinet  isi  elib  scopus
    4. Juric T., Meljanac S., Samsarov A., “Light-Like Kappa-Deformations and Scalar Field Theory Via Drinfeld Twist”, Conceptual and Technical Challenges For Quantum Gravity 2014 - Parallel Session: Noncommutative Geometry and Quantum Gravity, Journal of Physics Conference Series, 634, eds. Martinetti P., Wallet J., AmelinoCamelia G., IOP Publishing Ltd, 2015, 012005  crossref  isi  scopus
    5. Meljanac, Stjepan; Pachol, Anna; Pikutic, Danijel, “Twisted conformal algebra related to kappa-Minkowski space”, PHYSICAL REVIEW D, 92:10 (2015), 105015  crossref  mathscinet  elib  scopus
    6. Meljanac S., Kresic-Juric S., Martinic T., “The Weyl realizations of Lie algebras, and left-right duality”, J. Math. Phys., 57:5 (2016), 051704  crossref  mathscinet  zmath  isi  elib  scopus
    7. Juric T., Meljanac S., Samsarov A., “Twist deformations leading to $\kappa$-Poincaré Hopf algebra and their application to physics”, XXIII International Conference on Integrable Systems and Quantum Symmetries (ISQS-23), Journal of Physics Conference Series, 670, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2016, UNSP 012027  crossref  isi  scopus
    8. S. Meljanac, D. Meljanac, F. Mercati, D. Pikutic, “Noncommutative spaces and Poincaré symmetry”, Phys. Lett. B, 766 (2017), 181–185  crossref  isi  scopus
    9. S. Meljanac, Z. Skoda, M. Stojic, “Lie algebra type noncommutative phase spaces are Hopf algebroids”, Lett. Math. Phys., 107:3 (2017), 475–503  crossref  mathscinet  zmath  isi  scopus
    10. 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
    11. S. Meljanac, D. Meljanac, S. Mignemi, R. Strajn, “Snyder-type space times, twisted Poincaré algebra and addition of momenta”, Int. J. Mod. Phys. A, 32:28-29 (2017), 1750172  crossref  mathscinet  zmath  isi  scopus
    12. S. Meljanac, D. Meljanac, A. Pachol, D. Pikutic, “Remarks on simple interpolation between Jordanian twists”, J. Phys. A-Math. Theor., 50:26 (2017), 265201  crossref  mathscinet  zmath  isi  scopus
    13. J. Lukierski, Z. Skoda, M. Woronowicz, “On Hopf algebroid structure of kappa-deformed Heisenberg algebra”, Phys. Atom. Nuclei, 80:3 (2017), 576–585  crossref  isi  scopus
    14. J. Lukierski, “Kappa-deformations: historical developments and recent results”, XXIV International Conference on Integrable Systems and Quantum Symmetries (ISQS-24), Journal of Physics Conference Series, 804, IOP Publishing Ltd, 2017, UNSP 012028  crossref  isi  scopus
    15. J. Lukierski, D. Meljanac, S. Meljanac, D. Pikutic, M. Woronowicz, “Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach”, Phys. Lett. B, 777 (2018), 1–7  crossref  mathscinet  isi  scopus
    16. M. Daszkiewicz, “Two-particle system in Coulomb potential for twist-deformed space-time”, Phys. Scr., 93:8 (2018), 085202  crossref  mathscinet  isi  scopus
    17. Kuznetsova Zh. Toppan F., “On Light-Like Deformations of the Poincare Algebra”, Eur. Phys. J. C, 79:1 (2019), 27  crossref  isi  scopus
    18. Lukierski J. Meljanac S. Woronowicz M., “Quantum Twist-Deformed D=4 Phase Spaces With Spin Sector and Hopf Algebroid Structures”, Phys. Lett. B, 789 (2019), 82–87  crossref  mathscinet  zmath  isi  scopus
    19. 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
    20. Meljanac D., Meljanac S., Mignemi S., Strajn R., “Kappa-Deformed Phase Spaces, Jordanian Twists, Lorentz-Weyl Algebra, and Dispersion Relations”, Phys. Rev. D, 99:12 (2019), 126012  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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