κ-Deformations of D=4 Weyl and conformal symmetries

Lukierski, J.; Lyakhovsky, V. D.; Mozrzymas, Marek

doi:10.1016/s0370-2693(02)02001-4

Cited by 44 publications

(55 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The associated (3 + 1)D noncommutative spacetime, generalizing (49), is currently under investigation. Finally, we recall that other different quantum (A)dS deformations have been obtained by working in a conformal basis instead of a pure kinematical one, for instance, (3, 2) [100, 101] and (4, 2) [47,[102][103][104], and the Drinfel' d-Jimbo quantum AdS space at roots of unity has been worked out in [105]. Also, other fuzzy [106,107] and covariant [44] noncommutative (A)dS spacetimes have also been constructed.…”

Section: Discussionmentioning

confidence: 99%

Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

Ballesteros

Bruno

Herranz

2017

Advances in High Energy Physics

View full text Add to dashboard Cite

The -deformation of the (2 + 1)D anti-de Sitter, Poincaré, and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel' d-double and the Poisson-Lie structure underlying the -deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson-Lie algebras. As a consequence, the noncommutative (2 + 1)D spacetimes that generalize the -Minkowski space to the (anti-)de Sitter ones are obtained. Moreover, noncommutative 4D spaces of (time-like) geodesics can be defined, and they can be interpreted as a novel possibility to introduce noncommutative worldlines. Furthermore, quantum (anti-)de Sitter algebras are presented both in the known basis related to 2 + 1 quantum gravity and in a new one which generalizes the bicrossproduct one. In this framework, the quantum deformation parameter is related to the Planck length, and the existence of a kind of "duality" between the cosmological constant and the Planck scale is also envisaged.

show abstract

Section: Discussionmentioning

confidence: 99%

Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

Ballesteros

Bruno

Herranz

2017

Advances in High Energy Physics

View full text Add to dashboard Cite

show abstract

“…Examples Take : the original κ, tachyonic and light-cone deformations, respectively (see also [11,15,16,42] for earlier works in this context). We shall denote them U SO(3) iso (1,3) …”

Section: Remark 5 It Is Well Known That the Real Algebras U Iso(pq) mentioning

confidence: 99%

Unified description for $$\kappa $$ κ -deformations of orthogonal groups

Borowiec

Pachoł

2014

Eur. Phys. J. C

View full text Add to dashboard Cite

In this paper we provide universal formulas describing Drinfeld-type quantization of inhomogeneous orthogonal groups determined by a metric tensor of an arbitrary signature living in a spacetime of arbitrary dimension. The metric tensor does not need to be in diagonal form and κ-deformed coproducts are presented in terms of classical generators. It opens the possibility for future applications in deformed general relativity. The formulas depend on the choice of an additional vector field which parametrizes classical r -matrices. Non-equivalent deformations are then labeled by the corresponding type of stability subgroups. For the Lorentzian signature it covers three (non-equivalent) Hopf-algebraic deformations: time-like, space-like (a.k.a. tachyonic) and light-like (a.k.a. light-cone) quantizations of the Poincaré algebra. Finally the existence of the so-called Majid-Ruegg (non-classical) basis is reconsidered.

show abstract

“…[30,31]) with the extension of standard κ-deformed Minkowski space relations by the introduction of arbitrary constant four-vector τ µ :…”

Section: Discussion and Outlookmentioning

confidence: 99%