Theoretical Statistics and Mathematics Unit, ISI Delhi

Spectral triples and associated Connes-de Rham complex for the quantum $SU(2)$ and the quantum sphere

by Partha Sarathi Chakraborty and Arupkumar Pal

In this article, we take up the construction of spectral triples and associated calculus in the
context of $SU_q (2)$ and $S_{qc}$. In order to construct explicit spectral triples, we begin with the
computation of $K$-groups, and then from explicit generators we construct spectral triples which
induce generating elements in $K$-homology. Using these spectral triples, we compute a modified
version of the space of Connes-de Rham forms and the associated calculus. The space of $L^2$ forms
have also been described explicitly.

isid/ms/2002/20 [fulltext]

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