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Mathematics > Quantum Algebra

arXiv:2411.03102 (math)
[Submitted on 5 Nov 2024 (v1), last revised 12 Nov 2024 (this version, v2)]

Title:Levi-Civita connection on the irreducible quantum flag manifolds

Authors:Jyotishman Bhowmick, Bappa Ghosh, Andrey O. Krutov, Réamonn Ó Buachalla
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Abstract: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.
Comments: Minor errors fixed
Subjects: Quantum Algebra (math.QA); Mathematical Physics (math-ph); Operator Algebras (math.OA)
Cite as: arXiv:2411.03102 [math.QA]
  (or arXiv:2411.03102v2 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.2411.03102

Submission history

From: Bappa Ghosh [view email]
[v1] Tue, 5 Nov 2024 13:47:02 UTC (81 KB)
[v2] Tue, 12 Nov 2024 13:04:23 UTC (81 KB)
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