• Corpus ID: 249926713

Compact Quantum Homogeneous K\"ahler Spaces

  title={Compact Quantum Homogeneous K\"ahler Spaces},
  author={Biswarup Das and R'eamonn 'O Buachalla and Petr Somberg},
. Noncommutative K¨ahler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we introduce the notion of a compact quantum homogeneous K¨ahler space which gives a natural set of compatibility conditions between covariant K¨ahler structures and Woronowicz’s theory of compact quantum groups. Each such object admits a Hilbert space completion possessing a remarkably rich yet tractable structure. The… 



A Dolbeault-Dirac Spectral Triple for Quantum Projective Space.

The notion of a Kahler structure for a differential calculus was recently introduced by the second author as a framework in which to study the noncommutative geometry of the quantum flag manifolds.

Positive Line Bundles Over the Irreducible Quantum Flag Manifolds

Noncommutative Kahler structures were recently introduced by the third author as a framework for studying noncommutative Kahler geometry on quantum homogeneous spaces. It was subsequently observed

Noncommutative K\"ahler Structures on Quantum Homogeneous Spaces

Noncommutative complex structures on quantum homogeneous spaces

Principal Pairs of Quantum Homogeneous Spaces

We propose a simple but effective framework for producing examples of covariant faithfully flat (generalised) Hopf–Galois extensions from a nested pair of quantum homogeneous spaces. Our construction

Holomorphic Structures on the Quantum Projective Line

We show that much of the structure of the 2-sphere as a complex curve survives the q-deformation and has natural generalizations to the quantum 2-sphere—which, with additional structures, we identify

A Kodaira Vanishing Theorem for Noncommutative Kahler Structures

Using the framework of noncommutative K\"ahler structures, we generalise to the \nc setting the celebrated vanishing theorem of Kodaira for positive line bundles. The result is established under the

De Rham complex for quantized irreducible flag manifolds

CQG algebras: A direct algebraic approach to compact quantum groups

The purely algebraic notion of CQG algebra (algebra of functions on a compact quantum group) is defined. In a straightforward algebraic manner, the Peter-Weyl theorem for CQG algebras and the

Dirac Operators on Quantum Projective Spaces

We construct a family of self-adjoint operators DN, $${N\in{\mathbb Z}}$$ , which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space