K-Theory of Stable Generalized Operator Algebras

The Algebraic K-theory of Operator Algebras

We the study the algebraic K-theory of C∗-algebras, forgetting the topology. The main results include a proof that commutative C∗-algebras are K-regular in all degrees (that is, all their NKi-groups vanish) and extensions of the Fischer-Prasolov Theorem comparing algebraic and topological K-theory with finite coefficients.

K-theory for operator algebras. Classification of C∗-algebras

In this article we survey some of the recent goings-on in the classification programme of C-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott conjecture does not hold at its boldest. We review the construction of this object both by means of positive elements and via its recent interpretation using counta...

K-theory associated to vertex operator algebras

We introduce two K-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these K-theories, and construct a natural homomorphism from the VOA K-theory to the associative algebra K-theory.

Operator Theory and Operator Algebras

K-theory of C-algebras from One-dimensional Generalized Solenoids

We compute the K-groups of C-algebras arising from one-dimensional generalized solenoids. The results show that Ruelle algebras from one-dimensional generalized solenoids are one-dimensional generalizations of Cuntz-Krieger algebras.