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Remarks on simple interpolation between Jordanian twists. (English) Zbl 1370.81094

81R60 Noncommutative geometry in quantum theory
81R25 Spinor and twistor methods applied to problems in quantum theory
83A05 Special relativity
53D55 Deformation quantization, star products
16T05 Hopf algebras and their applications
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
14D15 Formal methods and deformations in algebraic geometry
Full Text: DOI
[1] Drinfeld V G 1985 Hopf algebras and the quantum Yang-Baxter equation Sov. Math.—Dokl.32 254
[2] Ogievetsky O 1994 Hopf structures on the Borel subalgebra of sl(2) Proc. of Winter School in Geometry and Physics(Zdikov, January 1993) p 185 · Zbl 0879.16027
[3] Tolstoy V N 2008 Twisted quantum deformations of Lorentz and Poincaré algebras Bulg. J. Phys.35 441-459 (arXiv:0712.3962) · Zbl 1202.81114
[4] Tolstoy V N 2007 Quantum deformations of relativistic symmetries Proc. of the 22nd Max Born Symp. on Quantum, Super and Twistors(Wroclaw, Poland, September 2006) (arXiv:0704.0081)
[5] Giaquinto A and Zhang J J 1998 Bialgebra actions, twists, and universal deformation formulas J. Pure Appl. Algebra128 133 · Zbl 0938.17015
[6] Borowiec A and Pachoł A 2009 κ-Minkowski spacetime as the result of Jordanian twist deformation Phys. Rev. D 79 045012
[7] Kovačević D, Meljanac S, Pachoł A and Štrajn R 2012 Generalized poincaré algebras, Hopf algebras and kappa-Minkowski spacetime Phys. Lett. B 711 122-7
[8] Kovačević D and Meljanac S 2012 κ-Minkowski spacetime, κ-Poincaré Hopf algebra and realiza-tions J. Phys. A: Math. Theor.45 135208 · Zbl 1241.83010
[9] Bu J G, Yee J H and Kim H C 2009 Differential structure on κ-Minkowski spacetime realized as module of twisted Weyl algebra Phys. Lett. B 679 486
[10] Lukierski J, Nowicki A, Ruegg H and Tolstoy V N 1991 Q-deformation of Poincaré algebra Phys. Lett. B 264 331
[11] Lukierski J, Nowicki A and Ruegg H 1992 New quantum Poincaré algebra and κ-deformed field theory Phys. Lett. B 293 344 · Zbl 0834.17022
[12] Meljanac S, Pachoł A and Pikutić D 2015 Twisted conformal algebra related to κ-Minkowski space Phys. Rev. D 92 105015
[13] Pachoł A and Vitale P 2015 κ-Minkowski star product in any dimension from symplectic realization J. Phys. A: Math. Theor.48 445202 · Zbl 1327.53111
[14] Borowiec A, Jurić T, Meljanac S and Pachoł A 2016 Central tetrads and quantum spacetimes Int. J. Geom. Methods Mod. Phys.13 1640005 · Zbl 1351.83020
[15] Kawaguchi I, Matsumoto T and Yoshida K 2014 Jordanian deformations of the AdS5×S5 superstring J. High Energy Phys.JHEP04(2014) 153
[16] Kawaguchi I, Matsumoto T and Yoshida K 2014 A Jordanian deformation of AdS space in type IIB supergravity J. High Energy Phys.JHEP06(2014) 146 · Zbl 1333.83195
[17] van Tongeren S J 2016 Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory Nucl. Phys. B 904 148-75 · Zbl 1332.81197
[18] Govindarajan T R, Gupta K S, Harikumar E, Meljanac S and Meljanac D 2008 Twisted statistics in kappa-Minkowski spacetime Phys. Rev. D 77 105010
[19] Jurić T, Meljanac S and Štrajn R 2014 Twists, realizations and Hopf algebroid structure of kappa-deformed phase space Int. J. Mod. Phys. A 29 1450022 · Zbl 1284.81175
[20] Jurić T, Kovačević D and Meljanac S 2014 κ-deformed phase space, Hopf algebroid and twisting SIGMA 10106 18 · Zbl 1310.81098
[21] Meljanac S, Škoda Z and Stojić M 2017 Lie algebra type noncommutative phase spaces are Hopf algebroids, accepted in letters in mathematical physics Lett. Math. Phys.107 475-503 · Zbl 1361.16015
[22] Meljanac S and Škoda Z 2016 Hopf algebroid twists for deformation quantization of linear Poisson structures (arXiv:1605.01376)
[23] Durov N, Meljanac S, Samsarov A and Škoda Z 2007 A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra J. Algebra309 318-59 · Zbl 1173.17014
[24] Meljanac S, Krešić-Jurić S and Martinić T 2016 The Weyl realizations of Lie algebras and left-right duality J. Math. Phys.57 051704 · Zbl 1342.58005
[25] Meljanac S, Krešić-Jurić S and Stojić M 2007 Covariant realizations of kappa-deformed space Eur. Phys. J. C 51 229 · Zbl 1189.81114
[26] Meljanac S and Stojić M 2006 New realizations of Lie algebra kappa-deformed Euclidean space Eur. Phys. J. C 47 531 · Zbl 1191.81138
[27] Meljanac S, Meljanac D, Samsarov A and Stojić M 2009 Lie algebraic deformations of Minkowski space with Poincaré algebra (arXiv:0909.1706)
[28] Meljanac S, Meljanac D, Samsarov A and Stojić M 2010 Kappa-deformed Snyder spacetime Mod. Phys. Lett. A 25 579-90 · Zbl 1188.83068
[29] Meljanac S, Meljanac D, Samsarov A and Stojić M 2011 Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra Phys. Rev. D 83 065009
[30] Meljanac S, Škoda Z and Svrtan D 2012 Exponential formulas and Lie algebra type star products SIGMA8 013 · Zbl 1248.81092
[31] Jurić T, Meljanac S and Pikutić D 2015 Realizations of κ-Minkowski space, Drinfeld twists and related symmetry algebras Eur. Phys. J. C 75 528
[32] Meljanac S, Meljanac D, Mercati F and Pikutić D 2017 Noncommutative spaces and Poincaré symmetry Phys. Lett. B 766 181-5 · Zbl 1397.81106
[33] Lukierski J, Škoda Z and Woronowicz M 2015 Deformed covariant quantum phase spaces as Hopf Algebroids Phys. Lett. B 750 401-6 · Zbl 1364.81170
[34] Jurić T, Meljanac S and Štrajn R 2013 κ-Poincaré-Hopf algebra and Hopf algebroid structure of phase space from twist Phys. Lett. A 377 2472-6 · Zbl 1311.81155
[35] Xu P 2001 Quantum groupoids Commun. Math. Phys.216 539-81 · Zbl 0986.17003
[36] Lu J 1996 Hopf algebroids and quantum groupoids Int. J. Math.7 47 · Zbl 0884.17010
[37] Böhm G and Szlachányi K 2004 Hopf algebroid symmetry of abstract frobenius extensions of depth 2 Commun. Algebra32 4433-64 · Zbl 1080.16036
[38] Böhm G 2008 Hopf algebroids (arXiv:0805.3806) · Zbl 1220.16022
[39] Borowiec A and Pachoł A 2017 Twisted bialgebroids versus bialgebroids from a Drinfeld twist J. Phys. A: Math. Theor.50 5 · Zbl 1357.81119
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