384 research outputs found
Torus equivariant spectral triples for odd dimensional quantum spheres coming from -extensions
The torus group has a canonical action on the odd
dimensional sphere . 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 -homology class thus
generalizing our earlier results for . We also relate the triple we
construct with the -extension
0\longrightarrow \clk\otimes C(S^1)\longrightarrow C(S_q^{2\ell+3})
\longrightarrow C(S_q^{2\ell+1}) \longrightarrow 0. Comment: LaTeX2e, 12 page
Equivariant spectral triples on the quantum SU(2) group
We characterize all equivariant odd spectral triples for the quantum SU(2)
group acting on its L_2-space and having a nontrivial Chern character. It is
shown that the dimension of an equivariant spectral triple is at least three,
and given any element of the K-homology group of SU_q(2), there is an
equivariant odd spectral triple of dimension 3 inducing that element. The
method employed to get equivariant spectral triples in the quantum case is then
used for classical SU(2), and we prove that for p<4, there does not exist any
equivariant spectral triple with nontrivial K-homology class and dimension p
acting on the L_2-space.Comment: LaTeX2e, 19 pages; v3:some results added in existing sections, one
new section on classical SU(2) added, two references added; v2:some typos and
one error correcte
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