No abstract

We investigate quantum lens spaces, C(L 2n+1 q (r; m)), introduced by Brzeziński-Szymański as graph C * -algebras. For n ≤ 3, we give a number-theoretic invariant, when all but one weight are coprime to the order of the acting group r. This builds upon the work of Eilers, Restorff, Ruiz and Sørensen.

We investigate quantum lens spaces, ( 2 +1 ( ; )), introduced by Brzeziński-Szymański as graph * -algebras. We give a new description of ( 2 +1 ( ; )) as graph * -algebras amending an error in the original paper by Brzeziński-Szymański. Furthermore, for ≤ 3, we give a number-theoretic invariant, when all but one weight are coprime to the order of the acting group . This builds upon the work of Eilers, Restorff, Ruiz and Sørensen.

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.

We investigate a quantum twistor bundle constructed as a U (1)-quotient of the quantum instanton bundle of Bonechi, Ciccoli and Tarlini. It is an example of a noncommutative bundle fulfilling conditions of the purely algebraic framework proposed by Brzeziński and Szymański. We provide a detailed description of the corresponding C * -algebra of 'continuous functions' on its noncommutative total space.