K-homology of the CAR algebra

Abstract

We compare the K-theory and K-homology of the well known CAR algebra. While the $K_0$ group is infinitely generated, we shows that it pairs identically to zero with even Fredholm modules over the algebra. We show further that in fact the even K-homology is trivial, while the odd K-homology is very large. These results give some insight into the K-homology of AF-algebras.