The $C^{\ast }$-algebra of the quantum symplectic sphere

Abstract

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

arXiv commentThe paper builds on the wrong statement in the paper "The quantum twistor bundle" Theorem 4.2. Therefore the C*-algebra investigated in the present paper is not the one for the quantum symplectic sphere