# Group theoretical construction of planar noncommutative phase spaces

@article{Ngendakumana2013GroupTC, title={Group theoretical construction of planar noncommutative phase spaces}, author={Ancille Ngendakumana and Joachim Nzotungicimpaye and Leonard Todjihounde}, journal={Journal of Mathematical Physics}, year={2013}, volume={55}, pages={013508} }

Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained…

## 13 Citations

### Conformal Carroll groups

- Mathematics
- 2014

Conformal extensions of Lévy–Leblondʼs Carroll group, based on geometric properties analogous to those of Newton–Cartan space-time are proposed. The extensions are labeled by an integer k. This…

### Planar Carrollean dynamics, and the Carroll quantum equation

- MathematicsJournal of Geometry and Physics
- 2022

### Kinematical versus dynamical contractions of the de Sitter Lie algebras

- Mathematics
- 2019

We present two kinematical Lie algebras contraction processes to improve the Bacry and Lévy-Leblond contractions ( H Bacry, et al , 1968 J. Math. Phys. , 9 , 1605 – 1614 ) : ( speed-time, speed-space…

### Carroll symmetry of plane gravitational waves

- Mathematics
- 2017

The well-known 5-parameter isometry group of plane gravitational waves in 4 dimensions is identified as Lévy-Leblond’s Carroll group in 2+1 dimensions with no rotations. Our clue is that plane waves…

### Anyonic spin-Hall effect on the black hole horizon

- PhysicsPhysical Review D
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Using the fact that the horizon of black holes is a Carroll manifold, we show that an “exotic photon” i.e. a mass and chargeless particle with anyonic spin, magnetic moment and “exotic” charges…

### Dynamics of Carroll particles

- Mathematics, Physics
- 2014

We investigate particles whose dynamics are invariant under the Carroll group. Although a single, free such Carroll particle has no non-trivial dynamics (the Carroll particle does not move), we show…

### Sturm–Liouville and Carroll: at the heart of the memory effect

- MathematicsGeneral Relativity and Gravitation
- 2018

For a plane gravitational wave whose profile is given, in Brinkmann coordinates, by a $$2\times 2$$2×2 symmetric traceless matrix K(U), the matrix Sturm–Liouville equation $$\ddot{P}=KP$$P¨=KP plays…

### Hall effects in Carroll dynamics

- Physics
- 2022

Do Carroll particles move?” The answer depends on the characteristics of the particle such as its mass, spin, electric charge, and magnetic moment. A massive Carroll particle (closely related to…

### A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

- Mathematics
- 2015

(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p…

### Kinematical versus dynamical contractions of the de Sitter Lie algebras

- MathematicsJournal of Physics Communications
- 2019

We present two kinematical Lie algebras contraction processes to improve the Bacry and Lévy-Leblond contractions (H Bacry, et al, 1968 J. Math. Phys., 9, 1605–1614) :(speed-time, speed-space and…

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