The K-theory of the triple-Toeplitz deformation of the complex projective plane

Abstract

We consider a family ${\pi }_j^i:B_i\to B_{ij}=B_{ji}$, $i,j\in \{1,2,3\}$, $i\ne j$, of $C^{\ast }$-epimorphisms assuming that it satisfies the cocycle condition. Then we show how to compute the $K$-groups of the multi-pullback $C^{\ast }$-algebra of such a family, and examplify it in the case of the triple-Toeplitz deformation of $\mathbb{C}{P}^2$.

7 pages