The C^*-algebra of the quantum symplectic sphere

2021/06/27 by Sophie Emma Zegers, Zegers, Sophie Emma
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2106.14209

openalex publication_date 2021/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The faithful irreducible *-representations of the C^*-algebra of the quantum symplectic sphere S_q^4n-1, n≥ 2, have been investigated by D'Andrea and Landi. They proved that the first n-1 generators are all zero inside C^*(S_q^4n-1), for n≥ 2. The result is a generalisation of the case where n=2, which was shown by Mikkelsen and Szymański. We will show that C^*(S_q^4n-1), n≥ 2 is isomorphic to a graph C^*-algebra. From here it follows that C^*(S_q^4n-1) is isomorphic to the quantum (2(n+1)-1)-sphere by Vaksman and Soibelman.

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