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

2007/01/25 by Partha Sarathi Chakraborty, Chakraborty, Partha Sarathi, Arupkumar Pal +1
Mathematics · #19K33 #46L87 #58B34 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.math/0701738

openalex publication_date 2007/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The torus group (S¹)^ℓ+1 has a canonical action on the odd dimensional sphere S_q^2ℓ+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⊗ C(S¹)\longrightarrow C(S_q^2ℓ+3) \longrightarrow C(S_q^2ℓ+1) \longrightarrow 0.

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