Levi-Civita connection on the irreducible quantum flag manifolds

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Bhowmick, Jyotishman, Ghosh, Bappa, Krutov, Andrey O., Buachalla, Réamonn Ó
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