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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 |
| Specialties: |
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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.
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.
Published as SciPost Phys. Proc. 14, 017 (2023)