Characterization of $SU_q(\ell+1)$-equivariant spectral triples for the odd dimensional quantum spheres

Partha Sarathi Chakraborty; Arupkumar Pal

Characterization of $SU_q(\ell+1)$-equivariant spectral triples for the odd dimensional quantum spheres

Quantum Algebra 2007-05-23 v1 K-Theory and Homology Operator Algebras

Authors: Partha Sarathi Chakraborty , Arupkumar Pal

Abstract

The quantum group $SU_q(\ell+1)$ has a canonical action on the odd dimensional sphere $S_q^{2\ell+1}$ . All odd spectral triples acting on the $L_2$ space of $S_q^{2\ell+1}$ and equivariant under this action have been characterized. This characterization then leads to the construction of an optimum family of equivariant spectral triples having nontrivial $K$ -homology class. These generalize the results of Chakraborty & Pal for $SU_q(2)$ .

Keywords

su_q(l+1) spectral triples quantum spheres equivariant k-homology

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@article{arxiv.math/0701694,
  title  = {Characterization of $SU_q(\ell+1)$-equivariant spectral triples for the odd dimensional quantum spheres},
  author = {Partha Sarathi Chakraborty and Arupkumar Pal},
  journal= {arXiv preprint arXiv:math/0701694},
  year   = {2007}
}

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Characterization of $SU_q(\ell+1)$-equivariant spectral triples for the odd dimensional quantum spheres

Abstract

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