Supersymmetry and Fredholm modules over quantized spaces

TL;DR

This paper applies non-commutative differential geometry to quantum deformations of Kahler manifolds, constructing Fredholm modules and computing Chern characters for specific quantum spaces.

Contribution

It introduces a novel framework for analyzing quantized Kahler manifolds using supersymmetric supercharges and Fredholm modules, with explicit formulas for Chern characters.

Findings

Fredholm modules constructed over quantized manifolds

Explicit Chern character formulas derived

Application to Cartan domains of type I and flat space

Abstract

The purpose of this paper is to apply the framework of non- commutative differential geometry to quantum deformations of a class of Kahler manifolds. For the examples of the Cartan domains of type I and flat space, we construct Fredholm modules over the quantized manifolds using the supercharges which arise in the quantization of supersymmetric generalizations of the manifolds. We compute the explicit formula for the Chern character on generators of the Toeplitz C^* -algebra.