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) $C^{\ast }$-algebra . We also work out several examples.

25 pages, latex

References in corpus (2)

• Lattices and Their Continuum Limits
• Noncommutative Lattices and the Algebra of their Continuous Functions