The $C^*$-algebra of the quantum symplectic sphere

Abstract

The faithful irreducible * -representations of the C * -algebra of the quantum symplectic sphere S 4n−1 q , n ≥ 2, have been investigated by D'Andrea and Landi. They proved that the first n − 1 generators are all zero inside C * (S 4n−1 q ), 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 4n−1 q ), n ≥ 2 is isomorphic to a graph C * -algebra. From here it follows that C * (S 4n−1 q ) is isomorphic to the quantum (2(n+1)−1)-sphere by Vaksman and Soibelman.