scholarly journals Quantum deformations of D = 4 Euclidean, Lorentz, Kleinian and quaternionico⋆(4)symmetries in unifiedo(4;C)setting

2016 ◽  
Vol 754 ◽  
pp. 176-181 ◽  
Author(s):  
A. Borowiec ◽  
J. Lukierski ◽  
V.N. Tolstoy
Keyword(s):  
Quantum Deformations

scholarly journals Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1309
Author(s):  
Jerzy Lukierski
Keyword(s):  
Phase Space ◽  
Hopf Algebras ◽  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Planck Length ◽  
Covariant Quantum ◽  
Drinfeld Twist ◽  
Quantum Deformations ◽  
Heisenberg Double ◽  
Conformal Symmetries

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras Uθ(su(2,2)⋉T4) and Uθ¯(su(2,2)⋉T¯4), where T4 describes complex twistor coordinates and T¯4 the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of D=4 Heisenberg-conformal algebra (HCA) su(2,2)⋉Hℏ4,4 (Hℏ4,4=T¯4⋉ℏT4 is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length λp, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in Hℏ4,4. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra Uθ(su(2,2)⋉T4).

scholarly journals 3d gravity and quantum deformations: a Drinfel'd double approach

2012 ◽  
Vol 360 ◽  
pp. 012010
Author(s):  
A Ballesteros ◽  
F J Herranz ◽  
C Meusburger
Keyword(s):  
Drinfel’D Double ◽  
Quantum Deformations ◽  
Double Approach ◽  
3D Gravity

scholarly journals Lie bialgebra contractions and quantum deformations of quasi‐orthogonal algebras

1995 ◽  
Vol 36 (10) ◽  
pp. 5916-5937 ◽  
Author(s):  
A. Ballesteros ◽  
N. A. Gromov ◽  
F. J. Herranz ◽  
M. A. del Olmo ◽  
M. Santander
Keyword(s):  
Lie Bialgebra ◽  
Quantum Deformations

New quantum deformations ofD=4 conformal algebra

1996 ◽  
Vol 46 (2-3) ◽  
pp. 217-225
Author(s):  
Jerzy Lukierski ◽  
Pierre Minnaert ◽  
Marek Mozrzymas
Keyword(s):  
Conformal Algebra ◽  
Quantum Deformations

Central elements of quantum deformations

2010 ◽  
Author(s):  
M. Havlíček ◽  
S. Pošta ◽  
Piotr Kielanowski ◽  
Victor Buchstaber ◽  
Anatol Odzijewicz ◽  
...  
Keyword(s):  
Central Elements ◽  
Quantum Deformations
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