Torus equivariant spectral triples for odd dimensional quantum spheres coming from C-extensions

Chakraborty, Partha Sarathi ; Pal, Arupkumar (2007) Torus equivariant spectral triples for odd dimensional quantum spheres coming from C-extensions Letters in Mathematical Physics, 80 (1). pp. 57-68. ISSN 0377-9017

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Official URL: http://www.springerlink.com/content/054327559416j5...

Related URL: http://dx.doi.org/10.1007/s11005-007-0149-z

Abstract

The torus group (S1)l+1 has a canonical action on the odd dimensional sphere Sq2l+1. We take the natural Hilbert space representation where this action is implemented and characterize all odd spectral triples acting on that space and equivariant with respect to that action. This characterization gives a construction of an optimum family of equivariant spectral triples having nontrivial K-homology class thus generalizing our earlier results for SUq(2). We also relate the triple we construct with the C-extension O→κ⊗C(S1)→C(Sq2l+3)→C(Sq2l+1)→O.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Spectral Triples; Noncommutative Geometry; Quantum Group
ID Code:89576
Deposited On:28 Apr 2012 12:50
Last Modified:19 May 2016 04:05

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