Levi-Civita connection on the irreducible quantum flag manifolds
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909385467363328 |
|---|---|
| author | Bhowmick, Jyotishman Ghosh, Bappa Krutov, Andrey O. Buachalla, Réamonn Ó |
| author_facet | Bhowmick, Jyotishman Ghosh, Bappa Krutov, Andrey O. Buachalla, Réamonn Ó |
| contents | We classify covariant metrics (in the sense of Beggs and Majid) on a class of quantum homogeneous spaces. In particular, our classification implies the existence of a unique (up to scalar) quantum symmetric covariant metric on the Heckenberger--Kolb calculi for the quantized irreducible flag manifolds. Moreover, we prove the existence and uniqueness of Levi-Civita connection for any real covariant metric for the Heckenberger--Kolb calculi. This generalizes Matassa's result for the quantum projective spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Levi-Civita connection on the irreducible quantum flag manifolds Bhowmick, Jyotishman Ghosh, Bappa Krutov, Andrey O. Buachalla, Réamonn Ó Quantum Algebra Mathematical Physics Operator Algebras We classify covariant metrics (in the sense of Beggs and Majid) on a class of quantum homogeneous spaces. In particular, our classification implies the existence of a unique (up to scalar) quantum symmetric covariant metric on the Heckenberger--Kolb calculi for the quantized irreducible flag manifolds. Moreover, we prove the existence and uniqueness of Levi-Civita connection for any real covariant metric for the Heckenberger--Kolb calculi. This generalizes Matassa's result for the quantum projective spaces. |
| title | Levi-Civita connection on the irreducible quantum flag manifolds |
| topic | Quantum Algebra Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2411.03102 |