Francesc Perera

THE CUNTZ SEMIGROUP, THE ELLIOTT CONJECTURE, AND DIMENSION FUNCTIONS ON C ∗ -ALGEBRAS

Abstract We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C*-algebras. In particular, our results apply to the largest class of simple C*-algebras for which K-theoretic classification can be hoped for. This work has three significant consequences. First, it provides new conceptual insight into Elliotts classification program, proving that the usual form of the Elliott conjecture is equivalent, among -stable algebras, to a conjecture which is in general substantially weaker and for which there are no known counterexamples. Second and third, it resolves, for the class of algebras above, two conjectures of Blackadar and Handelman concerning the basic structure of dimension functions on C*-algebras. We also prove in passing that the Cuntz-Pedersen semigroup is recovered functorially from the Elliott invariant for a large class of simple unital C*-algebras.

Chain conditions for Leavitt path algebras

Abstract In this paper we give necessary and sufficient conditions on a row-finite graph E so that the corresponding (not necessarily unital) Leavitt path K-algebra LK (E) is either artinian or noetherian from both a local and a categorical perspective. These extend the known results in the unital case to a much wider context. Besides the graph theoretic conditions, we provide in both situations isomorphisms between these algebras and appropriate direct sums of matrix rings over K or K[x, x –1].

COMPLETIONS OF MONOIDS WITH APPLICATIONS TO THE CUNTZ SEMIGROUP

We provide an abstract categorical framework that relates the Cuntz semigroups of the C

Multipliers of von neumann regular rings

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The Structure of Positive Elements for C*-Algebras with Real Rank Zero

-algebras

Tensor products and regularity properties of Cuntz semigroups

A

NON-SIMPLE PURELY INFINITE RINGS

and

RECOVERING THE ELLIOTT INVARIANT FROM THE CUNTZ SEMIGROUP

A\otimes \mathcal{K}

Computing the maximal algebra of quotients of a Lie algebra

. This is done through a certain completion of ordered monoids by adding suprema of countable ascending sequences. Our construction is rather explicit and we show it is functorial and unique up to isomorphism. This approach is used in some applications to compute the stabilized Cuntz semigroup of certain C

The Corona Factorization Property and refinement monoids

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