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

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

2007-01-24

arxiv.org/abs/math/0701694v1

Mathematics

Quantum Algebra

LaTeX2e, 20 pages

Scientific paper

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 $SU_q(2)$.

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