2008/11/24 by Arupkumar Pal, Pal, Arupkumar, S. Sundar +1 · 3 citations
Mathematics · #19K33 #46L87 #58B34 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.0811.3810
openalex publication_date 2008/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The odd dimensional quantum sphere Sq2ℓ+1 is a homogeneous space for the quantum group SUq(ℓ+1). A generic equivariant spectral triple for Sq2ℓ+1 on its L2 space was constructed by Chakraborty & Pal. We prove regularity for that spectral triple here. We also compute its dimension spectrum and show that it is simple. We give detailed construction of its smooth function algebra and some related algebras that help proving regularity and in the computation of the dimension spectrum. Following the idea of Connes for SUq(2), we first study another spectral triple for Sq2ℓ+1 equivariant under torus group action constructed by Chakraborty & Pal. We then derive the results for the SUq(ℓ+1)-equivariant triple in the q=0 case from those for the torus equivariant triple. For the q≠ 0 case, we deduce regularity and dimension spectrum from the q=0 case.