Isomorphisms of quantum spheres

2024/06/25 by Francesco D’Andrea, D'Andrea, Francesco
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Primary: 16T20 #Quantum Algebra (math.QA) #Secondary: 20G42

paper · pdf · doi:10.48550/arxiv.2406.17288

openalex publication_date 2024/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For n∈ℕ and q∈ [0,1[, the Vaksman-Soibelman quantum sphere S²ⁿ⁺¹_q is described by an associative algebra A(S²ⁿ⁺¹_q) deforming the algebra of polynomial functions on the 2n+1 dimensional unit sphere. Its C*-enveloping algebra is known to be independent of the deformation parameter q. In contrast to what happens in the C*-algebraic setting, we show here that, for all q,q' in the above range, A(S²ⁿ⁺¹_q) is isomorphic to A(S²ⁿ⁺¹_q') only if q=q'.

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