Regularity and dimension spectrum of the equivariant spectral triple for the odd-dimensional quantum spheres
Arupkumar Pal
Indian Statistical Institute, New DelhiS. Sundar
Institute of Mathematical Sciences, Chennai
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Abstract
The odd-dimensional quantum sphere is a homogeneous space for the quantum group . A generic equivariant spectral triple for on its -space was constructed by Chakraborty and Pal in [4]. We prove regularity for that spectral triple here. We also compute its dimension spectrum and show that it is simple. We give a detailed construction of its smooth function algebra and some related algebras that help proving regularity and in the computation of the dimension spectrum. Following the idea of Connes for , we first study another spectral triple for equivariant under torus group action and constructed by Chakraborty and Pal in [3]. We then derive the results for the -equivariant triple in the case from those for the torus equivariant triple. For the case , we deduce regularity and dimension spectrum from the case .
Cite this article
Arupkumar Pal, S. Sundar, Regularity and dimension spectrum of the equivariant spectral triple for the odd-dimensional quantum spheres. J. Noncommut. Geom. 4 (2010), no. 3, pp. 389–439
DOI 10.4171/JNCG/61