Quantum double suspension and spectral triples

Chakraborty, Partha Sarathi ; Sundar, S. (2011) Quantum double suspension and spectral triples Journal of Functional Analysis, 260 (9). pp. 2716-2741. ISSN 0022-1236

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Official URL: https://www.sciencedirect.com/science/article/pii/...

Related URL: http://dx.doi.org/10.1016/j.jfa.2011.01.009

Abstract

In this paper we are concerned with the construction of a general principle that will allow us to produce regular spectral triples with finite and simple dimension spectrum. We introduce the notion of weak heat kernel asymptotic expansion (WHKAE) property of a spectral triple and show that the weak heat kernel asymptotic expansion allows one to conclude that the spectral triple is regular with finite simple dimension spectrum. The usual heat kernel expansion implies this property. The notion of quantum double suspension of a C*-algebra was introduced by Hong and Szymanski. Here we introduce the quantum double suspension of a spectral triple and show that the WHKAE is stable under quantum double suspension. Therefore quantum double suspending compact Riemannian spin manifolds iteratively we get many examples of regular spectral triples with finite simple dimension spectrum. This covers all the odd-dimensional quantum spheres. Our methods also apply to the case of noncommutative torus.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Local Index Formula; Regularity; Dimension Spectrum; Heat Kernel Expansion; Quantum Double Suspension
ID Code:112443
Deposited On:05 Jun 2018 06:33
Last Modified:05 Jun 2018 06:33

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