Supersymmetry and Fredholm Modules Over Quantized Spaces

• Type of Material: Article
• Authors: David Borthwick, Emory University; Slawomir Klimek, Indiana University; Andrzej Lesniewski, Harvard University; Maurizio Rinaldi, Harvard University
• Language: English
• Date: 1994
• Publisher: Springer Verlag (Germany)
• Publication Version: Preprint (Prior to Peer Review)
• Copyright Statement: © Springer-Verlag 1994
• Final Published Version (URL): http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1007%2FBF02112322&v=e4e34f82
• Title of Journal or Parent Work: Communications in Mathematical Physics
• ISSN: 0010-3616
• Volume: 166
• Start Page: 397
• End Page: 416
• Grant/Funding Information: Supported in part by the National Science Foundation under grant DMS–9206936. Supported in part by the Department of Energy under grant DE–FG02–88ER25065. Supported in part by the Consiglio Nazionale delle Ricerche (CNR).
• Research Categories: Mathematics

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.