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Chakraborty, Partha Sarathi; Pal, Arupkumar (2007)
Languages: English
Types: Preprint
Subjects: 58B34, 46L87, 19K33, Mathematics - Operator Algebras, Mathematics - K-Theory and Homology, Mathematics - Quantum Algebra

Classified by OpenAIRE into

arxiv: Mathematics::K-Theory and Homology, Mathematics::Operator Algebras
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 \[ 0\longrightarrow \clk\otimes C(S^1)\longrightarrow C(S_q^{2\ell+3}) \longrightarrow C(S_q^{2\ell+1}) \longrightarrow 0. \]
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    • [4] Chakraborty, P. S. ; Pal, A. : Spectral triples and associated Connes-de Rham complex for the quantum SU (2) and the quantum sphere, arXiv:math.QA/0210049, Commun. Math. Phys., 240(2003), No. 3, 447-456.
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