Operator algebras and algebraic $K$-theory

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.

Algebraic Quantum Field Theory and Operator Algebras

In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as " why mathematicians are/should be interested in algebraic quantum field theory " would be equally fitting. Besides a presentation of the framework and the main results of local quantum physics these notes may s...

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.

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...

Operator Theory and Operator Algebras