K-Theory of Noncommutative Lattices

Abstract

Noncommutative lattices have been recently used as finite topological approximations in quantum physical models. As a first step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their K-theory. We shall do it algebraically, by studying the algebraic K-theory of the associated algebras of ‘continuous functions’ which turn out to be noncommutative approximately finite dimensional (AF) C ∗ -algebra . We also work out several examples.