Noncommutative Deformations of Locally Symmetric Kähler manifolds

Abstract

We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric Kähler manifold. This quantization method is one of the ways to perform a deformation quantization of Kähler manifolds, which is introduced by Karabegov. From the recurrence relations, concrete expressions of star products for one-dimensional local symmetric Kähler manifolds and $\mathbb{C}{P}^N$ are constructed. The recurrence relations for a Grassmann manifold $G_{2,2}$ are closely studied too.

arXiv comment25pages. Typos in Theorem 3.5, Proposition 4.1, and so on are corrected

References in corpus (8)

• Deformation quantization of Poisson manifolds, I
• Fuzzy spaces, the M(atrix) model and the quantum Hall effect
• The deformation quantizations of the hyperbolic plane
• A New Noncommutative Product on the Fuzzy Two-Sphere Corresponding to the Unitary Representation of SU(2) and the Seiberg-Witten Map
• An explicit formula for a star product with separation of variables
• Algebra of Noncommutative Riemann Surfaces
• Twisted Fock Representations of Noncommutative Kähler Manifolds
• Gauge theories on noncommutative $\mathbb{C}{P}^N$ and BPS-like equations