Kähler structures on quantum irreducible flag manifolds

Abstract

We prove that all quantum irreducible flag manifolds admit Kähler structures, as defined by Ó Buachalla. In order to show this result, we also prove that the differential calculi defined by Heckenberger and Kolb are differential *-calculi in a natural way.

arXiv commentv2: some errors corrected, main result slightly weakened

References in corpus (3)

• Supersymmetric quantum theory and non-commutative geometry
• Holomorphic structures on the quantum projective line
• Quantized flag manifolds and irreducible *-representations

Cited by in corpus (9)

• Holomorphic Relative Hopf Modules over the Irreducible Quantum Flag Manifolds
• Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
• An algebraic framework for noncommutative bundles with homogeneous fibres
• Covariant connections on bicovariant differential calculus
• Crystal limits of compact semisimple quantum groups as higher-rank graph algebras
• Quantum Riemannian geometry of quantum projective spaces
• Twisted Hochschild Homology of Quantum Flag Manifolds and Kähler Forms
• Equivariant quantizations of the positive nilradical and covariant differential calculi
• Fubini-Study metrics and Levi-Civita connections on quantum projective spaces