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

scholarly journals κ-DEFORMATIONS OF D = 3 CONFORMAL VERSUS DEFORMATIONS OF D = 4 AdS SYMMETRIES

2003 ◽  
Vol 18 (11) ◽  
pp. 753-769 ◽  
Author(s):  
J. LUKIERSKI ◽  
V. D. LYAKHOVSKY ◽  
M. MOZRZYMAS
Keyword(s):  
Hopf Algebra ◽  
Conformal Algebra ◽  
Drinfeld Twist ◽  
Deformation Parameters ◽  
Quantum Deformations

We describe the classical o(3,2)r-matrices as generating the quantum deformations of either D = 3 conformal algebra with mass-like deformation parameters or D = 4 AdS algebra with dimensionless deformation parameters. We describe the quantization of classical o(3,2)r-matrices via Drinfeld twist method which locates the deformation in the coalgebra sector. Further we obtain the quantum o(3,2) algebra in a convenient Hopf algebra form by considering suitable deformation maps from classical to deformed o(3,2) algebra basis. It appears that if we pass from κ-deformed D = 3 conformal algebra basis, to the deformed D = 4 AdS generators basis, the role of dimensionful parameter is taken over by the AdS radius R. We also provide the bilinear o(3,2) Casimir which we express using the deformed D = 3 conformal basis.

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).

TOPOLOGICAL CONFORMAL ALGEBRA IN POLYAKOV’S LIGHT-CONE GAUGE GRAVITY

1992 ◽  
Vol 07 (35) ◽  
pp. 3291-3302 ◽  
Author(s):  
KIYONORI YAMADA
Keyword(s):  
Light Cone ◽  
Matter Field ◽  
Conformal Algebra ◽  
Two Dimensional ◽  
Topological Algebras ◽  
Light Cone Gauge ◽  
Brst Cohomology ◽  
Dimensional Gravity ◽  
Conformal Gauge ◽  
Gauge Gravity

We show that the two-dimensional gravity coupled to c=−2 matter field in Polyakov’s light-cone gauge has a twisted N=2 superconformal algebra. We also show that the BRST cohomology in the light-cone gauge actually coincides with that in the conformal gauge. Based on this observation the relations between the topological algebras are discussed.

scholarly journals Lie Super-bialgebra Structures on the Centerless Twisted N=2 Super-conformal Algebra

2011 ◽  
Vol 18 (03) ◽  
pp. 361-372 ◽  
Author(s):  
Huanxia Fa ◽  
Junbo Li ◽  
Bin Xin
Keyword(s):  
Conformal Algebra

In this paper, Lie super-bialgebra structures on the centerless twisted N=2 super-conformal algebra [Formula: see text] are considered, which are proved to be coboundary triangular.

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 Loop Schrödinger–Virasoro Lie conformal algebra

2016 ◽  
Vol 27 (06) ◽  
pp. 1650057 ◽  
Author(s):  
Haibo Chen ◽  
Jianzhi Han ◽  
Yucai Su ◽  
Ying Xu
Keyword(s):  
Lie Algebra ◽  
Conformal Algebra ◽  
Cohomology Groups ◽  
Conformal Algebras ◽  
Rank One ◽  
Intermediate Series

In this paper, we introduce two kinds of Lie conformal algebras, associated with the loop Schrödinger–Virasoro Lie algebra and the extended loop Schrödinger–Virasoro Lie algebra, respectively. The conformal derivations, the second cohomology groups of these two conformal algebras are completely determined. And nontrivial free conformal modules of rank one and [Formula: see text]-graded free intermediate series modules over these two conformal algebras are also classified in the present paper.

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

scholarly journals The N = 4 quantum conformal algebra

1999 ◽  
Vol 541 (1-2) ◽  
pp. 369-385 ◽  
Author(s):  
Damiano Anselmi
Keyword(s):  
Conformal Algebra
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