One of the main tools to classify C∗-algebras is the study of its projections and its unitaries. It was proved by Cuntz in [Cun81] that if A is a purely infinite simple C∗-algebra, then the kernel of the natural map for the unitary group U(A) to the Ktheory groupK1(A) is reduced to the connected component U(A), i.e. A isK1-injective (see §3). We study in this note a finitely generated C∗-algebr...

We introduce a wide class of countable groups, called properly proximal, which contains all non-amenable bi-exact non-elementary convergence and lattices in non-compact semi-simple Lie but excludes inner amenable groups. show that crossed product II$_1$ factors arising from free ergodic probability measure preserving actions groups this have at most one weakly compact Cartan subalgebra, up to u...

The MIS Quarterly has always had a strong focus on building and testing theory. In this regard, most research articles published in the MIS Quarterly have proposed a theory and then tested it either in whole or in part. In the June 1998 issue of the MIS Quarterly, however, Bob Zmud as then Editor-in-Chief issued a call for pure-theory submissions: research article submissions that had the sole ...

one will no doubt be as successful as its predecessors. It lacks something in connected thought, for its "chapters" are in reality different lectures given to a wide variety of audiences and necessarily pitched at different levels under titles by no means mutually exclusive. The book is thus best read as a series of essays and these include, as in the author's other writings, sex and society, t...