Papers on quantum spheres

Here are two papers that I have uploaded to the arxiv recently:

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

Authors: Partha Sarathi Chakraborty, Arupkumar Pal
Comments: LaTeX2e, 20 pages
Subj-class: Quantum Algebra; K-Theory and Homology; Operator Algebras
MSC-class: 58B34, 46L87, 19K33

The quantum group has a canonical action on the odd dimensional sphere . All odd spectral triples acting on the space of 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 -homology class. These generalize the results of Chakraborty & Pal for .

Source: http://arxiv.org/abs/math.QA/0701694

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

Authors: Partha Sarathi Chakraborty, Arupkumar Pal
Comments: LaTeX2e, 12 pages
Subj-class: K-Theory and Homology; Operator Algebras; Quantum Algebra
MSC-class: 58B34, 46L87, 19K33

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 .

Source: http://arxiv.org/abs/math.KT/0701738

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