1. CMB Online first
 Boutonnet, Remi; Roydor, Jean

A note on uniformly bounded cocycles into finite von Neumann algebras
We give a short proof of a result of T. Bates
and T. Giordano stating that any uniformly bounded Borel cocycle
into a finite von Neumann algebra is cohomologous to a unitary
cocycle. We also point out a separability issue in
their proof. Our approach is based on the existence of a nonpositive
curvature metric on the positive cone of a finite von Neumann
algebra.
Keywords:Borel cocycle, von Neumann algebra Categories:46L55, 46L40, 22D40 

2. CMB 2006 (vol 49 pp. 371)
 Floricel, Remus

Inner $E_0$Semigroups on Infinite Factors
This paper is concerned with the structure of
inner $E_0$semigroups. We show that any inner
$E_0$semigroup acting on an infinite factor
$M$ is completely determined by a continuous
tensor product system of Hilbert spaces in
$M$ and that the product system associated
with an inner $E_0$semigroup is a complete cocycle conjugacy invariant.
Keywords:von Neumann algebras, semigroups of endomorphisms, product systems, cocycle conjugacy Categories:46L40, 46L55 

3. CMB 2003 (vol 46 pp. 509)
 Benson, David J.; Kumjian, Alex; Phillips, N. Christopher

Symmetries of Kirchberg Algebras
Let $G_0$ and $G_1$ be countable abelian groups. Let $\gamma_i$ be an
automorphism of $G_i$ of order two. Then there exists a unital
Kirchberg algebra $A$ satisfying the Universal Coefficient Theorem and
with $[1_A] = 0$ in $K_0 (A)$, and an automorphism $\alpha \in
\Aut(A)$ of order two, such that $K_0 (A) \cong G_0$, such that $K_1
(A) \cong G_1$, and such that $\alpha_* \colon K_i (A) \to K_i (A)$ is
$\gamma_i$. As a consequence, we prove that every
$\mathbb{Z}_2$graded countable module over the representation ring $R
(\mathbb{Z}_2)$ of $\mathbb{Z}_2$ is isomorphic to the equivariant
$K$theory $K^{\mathbb{Z}_2} (A)$ for some action of $\mathbb{Z}_2$ on
a unital Kirchberg algebra~$A$.
Along the way, we prove that every not necessarily finitely generated
$\mathbb{Z} [\mathbb{Z}_2]$module which is free as a
$\mathbb{Z}$module has a direct sum decomposition with only three
kinds of summands, namely $\mathbb{Z} [\mathbb{Z}_2]$ itself and
$\mathbb{Z}$ on which the nontrivial element of $\mathbb{Z}_2$ acts
either trivially or by multiplication by $1$.
Categories:20C10, 46L55, 19K99, 19L47, 46L40, 46L80 

4. CMB 2003 (vol 46 pp. 365)
5. CMB 2001 (vol 44 pp. 335)
 Stacey, P. J.

Inductive Limit Toral Automorphisms of Irrational Rotation Algebras
Irrational rotation $C^*$algebras have an inductive limit
decomposition in terms of matrix algebras over the space of continuous
functions on the circle and this decomposition can be chosen to be
invariant under the flip automorphism. It is shown that the flip is
essentially the only toral automorphism with this property.
Categories:46L40, 46L35 
