Exact C*-Algebras, Tensor Products, and the Classification of Purely Infinite Algebras

Our survey (and the reference list) does not reflect the history of tensor products of operator algebras. Here we make use of tensor product functors on the category of C-algebras as a unifying principle. An application of our theory to the classification problem of Elliott [13] can be found at the end of this paper. Throughout the paper algebra means C*-algebra and vN - algebra means von Neumann algebra. L ( H ) is the algebra of bounded operators on a Hilbert space of infinite dimension.