Note on Kasparov Product of $C^*$-algebra Extensions

http://dx.doi.org/10.4153/CMB-2012-001-3
12 pages

  Published:2012-03-05
 

Using the Dadarlat isomorphism, we give a characterization for the Kasparov product of $C^*$-algebra extensions. A certain relation between $KK(A, \mathcal q(B))$ and $KK(A, \mathcal q(\mathcal k B))$ is also considered when $B$ is not stable and it is proved that $KK(A, \mathcal q(B))$ and $KK(A, \mathcal q(\mathcal k B))$ are not isomorphic in general.