TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysProc.14.017
TI  - A general approach to noncommutative spaces from Poisson homogeneous spaces: Applications to (A)dS and Poincaré
PY  - 2023/11/23
UR  - https://scipost.org/SciPostPhysProc.14.017
JF  - SciPost Physics Proceedings
JA  - SciPost Phys. Proc.
VL  - 
IS  - 14
SP  - 017
A1  - Ballesteros, Angel
AU  - Guitérrez-Sagredo, Iván
AU  - Herranz, Francisco J.
AB  - In this contribution we present a general procedure that allows the construction of noncommutative spaces with quantum group invariance as the quantization of their associated coisotropic Poisson homogeneous spaces coming from a coboundary Lie bialgebra structure. The approach is illustrated by obtaining in an explicit form several noncommutative spaces from (3+1)D (A)dS and Poincaré coisotropic Lie bialgebras. In particular, we review the construction of the $\kappa$-Minkowski and $\kappa$-(A)dS spacetimes in terms of the cosmological constant L. Furthermore, we present all noncommutative Minkowski and (A)dS spacetimes that preserve a quantum Lorentz subgroup. Finally, it is also shown that the same setting can be used to construct the three possible 6D $\kappa$-Poincaré spaces of time-like worldlines. Some open problems are also addressed.
ER  -

@Article{10.21468/SciPostPhysProc.14.017,
	title={{A general approach to noncommutative spaces from Poisson homogeneous spaces: Applications to (A)dS and Poincaré}},
	author={Angel Ballesteros and Ivan Guitérrez-Sagredo and Francisco J. Herranz},
	journal={SciPost Phys. Proc.},
	pages={017},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysProc.14.017},
	url={https://scipost.org/10.21468/SciPostPhysProc.14.017},
}