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A general approach to noncommutative spaces from Poisson homogeneous spaces: Applications to (A)dS and Poincaré
by Angel Ballesteros, Ivan Gutierrez-Sagredo and Francisco J. Herranz
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Francisco J. Herranz |
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| Preprint Link: | scipost_202212_00061v2 (pdf) |
| Date accepted: | 2023-08-11 |
| Date submitted: | 2023-02-15 10:26 |
| Submitted by: | Herranz, Francisco J. |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022) |
| Ontological classification | |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
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 Poincar\'e coisotropic Lie bialgebras. In particular, we review the construction of the $\kappa$-Minkowski and $\kappa$-(A)dS spacetimes in terms of the cosmological constant $\Lambda$. Furthermore, we present all noncommutative Minkowski and (A)dS spacetimes that preserved a quantum Lorentz subgroup. Finally, it is also shown that the same setting can be used to construct the three possible 6D $\kappa$-Poincar\'e spaces of time-like worldlines. Some open problems are also addressed.
Published as SciPost Phys. Proc. 14, 017 (2023)
Author comments upon resubmission
List of changes
In accordance with the referee's report, we have briefly commented on the representations on page 4 after eq. (15). Some typos have been corrected.