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A general approach to noncommutative spaces from Poisson homogeneous spaces: Applications to (A)dS and Poincar\'e
by Angel Ballesteros, Ivan Gutierrez-Sagredo and Francisco J. Herranz
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Submission summary
| Authors (as registered SciPost users): | Francisco J. Herranz |
| Submission information | |
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| Preprint Link: | scipost_202212_00061v1 (pdf) |
| Date submitted: | 2022-12-22 15:15 |
| 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.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2023-1-25 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202212_00061v1, delivered 2023-01-24, doi: 10.21468/SciPost.Report.6601
Strengths
1. The paper provides a rigorous construction of a number of nontrivial, noncommutative, associative algebras starting from classical, geometric structures based on Lie groups.
2. The presentation is concise and clear with all basic ingredients defined carefully and many examples worked out explicitly.
Weaknesses
1. The algebras are described only in the defining, or adjoint, representation, whereas it would h have been interesting if the authors could have commented on the existence of other representations, for example by factoring out nontrivial ideals.
Report
I find that the paper meets the criteria for publication in the journal.