More about the q-deformed Poincaré algebra

Giller, Stefan; Kosiński, Piotr; Majewski, M.; Maślanka, P.; Kunz, Jutta

doi:10.1016/0370-2693(92)90158-z

Cited by 129 publications

(126 citation statements)

References 5 publications

Supporting

Mentioning

125

Contrasting

Order By: Relevance

“…These results are presented in the kinematical basis in which they were formerly obtained [19], and the contraction = 0 gives the -Poincaré written in the form deduced in [13]. We also point out some remarks concerning the connection between these structures and quantum gravity that has been introduced in [38].…”

Section: Quantum (Anti-)de Sitter Algebrasmentioning

confidence: 76%

“…The first-order deformation terms in the coproduct of thePoincaré algebra [9,[13][14][15][16][17][18]22] are known to be generated by the following classical -matrix:…”

Section: (Anti-)de Sitter Drinfel'd-doubles and First-order Noncommutmentioning

confidence: 99%

“…Quantum deformations of Lie algebras and Lie groups [2][3][4][5][6][7][8] have been broadly applied in the construction of deformed symmetries of spacetimes [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], especially for the Poincaré and Galilei cases, for which the deformation parameter is known to play the role of a fundamental scale. Among all these quantum kinematical algebras the well known -Poincaré algebra [9,13,14,16,18] has been frequently considered.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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: Quantum (Anti-)de Sitter Algebrasmentioning

confidence: 76%

“…The first-order deformation terms in the coproduct of thePoincaré algebra [9,[13][14][15][16][17][18]22] are known to be generated by the following classical -matrix:…”

Section: (Anti-)de Sitter Drinfel'd-doubles and First-order Noncommutmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

“…First we recall here the basic formulae describing the quantum deformation of the D = 4 P oincar e algebra with a fundamental mass-like parameter [4,[7][8][9][10]. The quantum deformations are described by a noncocommutative Hopf algebra with its algebra and coalgebra sectors and with the notions of antipodes and a counit [1][2][3].…”

Section: {Deformed Quantum Poincar E Algebramentioning

confidence: 99%

“…Recently, many proposals were presented showing how to apply the ideas of quantum deformations [1][2][3] to the D = 4 P oincar e algebra [4][5][6][7][8][9][10] as well as the D = 4 P oincar e group [11][12][13][14][15][16]. The -deformation of the D = 4 P oincar e algebra, rst proposed in [4,8], leads to the modication of relativistic symmetries with the three-dimensional E(3) subalgebra unchanged.…”

Section: Introductionmentioning

confidence: 99%