Noncommutative Geometry and Topology in Prague

Split extensions and KK-equivalences for quantum projective spaces

In this talk, I will present an explicit KK-equivalence between the noncommutative C^*-algebra of continuous functions on the Vaksman–Soibelman quantum complex projective space C(\mathbb{C}P_q^n) and the commutative algebra \mathbb{C}^{n+1}. The KK-equivalence is constructed by finding an explicit splitting for the short exact sequence of C^*-algebras \mathcal{K}\to C(\mathbb{C}P_q^n)\to C(\mathbb{C}P_q^{n-1}). In the construction of the splitting it is crucial that C(\mathbb{C}P_q^n) can be described as a graph C^*-algebra due to Hong and Szymański. 

This talk is based on joint work with Francesca Arici.