Theoretical Statistics and Mathematics Unit, ISI Delhi

Torus equivariant spectral triples for odd dimensional quantum spheres coming from $C^*$-extensions

by Partha Sarathi Chakraborty and Arupkumar Pal

The torus group $(S^1)^{\ell+1}$ has a canonical action
on the odd dimensional sphere $S_q^{2\ell+1}$.
We take the natural Hilbert space representation
where this action is implemented and characterize
all odd spectral triples acting on that space and equivariant
with respect to that action.
This characterization gives a construction of
an optimum family of equivariant spectral triples having
nontrivial $K$-homology class thus generalizing our earlier results
for $SU_q(2)$. We also relate
the triple we construct with the $C^*$-extension
\[
0\longrightarrow \mathcal{K}\otimes C(S^1)\longrightarrow C(S_q^{2\ell+3})
\longrightarrow C(S_q^{2\ell+1}) \longrightarrow 0.
\]

isid/ms/2007/02 [fulltext]

Click here to return to Preprints Page