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K-Theory of Noncommutative Lattices

Elisa Ercolessi·Giovanni Landi·Paulo Teotonio-Sobrinho
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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.

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Elisa Ercolessi, Giovanni Landi, Paulo Teotonio-Sobrinho. 1996-07-17. K-Theory of Noncommutative Lattices. https://arxiv.org/abs/q-alg/9607017

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