Regularity and dimension spectrum of the equivariant spectral triple for the odd dimensional quantum spheres

By Arupkumar Pal, S. Sundar. 2008

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The odd dimensional quantum sphere S 2l+1 q is a homogeneous space for the quantum group SUq(l + 1). A generic equivariant spectral triple for S 2l+1 q on its L2 space was constructed by Chakraborty & 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 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 SUq(2), we first study another spectral triple for S 2l+1 q equivariant under torus group action constructed by Chakraborty & Pal in [3]. We then derive the results for the SUq(l+ 1)-equivariant triple in the q = 0 case from those for the torus equivariant triple. For the q 6 0 case, we deduce regularity and dimension spectrum from the q = 0 case.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/277b06cad11e929504d5e26c40e0176c03aa2305

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Citations in the corpus

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