1. CMB 2012 (vol 56 pp. 534)
 Filali, M.; Monfared, M. Sangani

A Cohomological Property of $\pi$invariant Elements
Let $A$ be a Banach algebra and $\pi \colon A \longrightarrow \mathscr L(H)$
be a continuous representation of $A$ on a separable Hilbert space $H$
with $\dim H =\frak m$. Let $\pi_{ij}$ be the coordinate functions of
$\pi$ with respect to an orthonormal basis and suppose that for each
$1\le j \le \frak m$, $C_j=\sum_{i=1}^{\frak m}
\\pi_{ij}\_{A^*}\lt \infty$ and $\sup_j C_j\lt \infty$. Under these
conditions, we call an element $\overline\Phi \in l^\infty (\frak m , A^{**})$
left $\pi$invariant if $a\cdot \overline\Phi ={}^t\pi (a) \overline\Phi$ for all
$a\in A$. In this paper we prove a link between the existence
of left $\pi$invariant elements and the vanishing of certain
Hochschild cohomology groups of $A$. Our results extend an earlier
result by Lau on $F$algebras and recent results of KaniuthLauPym
and the second named author in the special case that $\pi \colon A
\longrightarrow \mathbf C$ is a nonzero character on $A$.
Keywords:Banach algebras, $\pi$invariance, derivations, representations Categories:46H15, 46H25, 13N15 

2. CMB 2009 (vol 53 pp. 77)
3. CMB 2009 (vol 52 pp. 535)
 Daigle, Daniel; Kaliman, Shulim

A Note on Locally Nilpotent Derivations\\ and Variables of $k[X,Y,Z]$
We strengthen certain results
concerning actions of $(\Comp,+)$ on $\Comp^{3}$
and embeddings of $\Comp^{2}$ in $\Comp^{3}$,
and show that these results are in fact valid
over any field of characteristic zero.
Keywords:locally nilpotent derivations, group actions, polynomial automorphisms, variable, affine space Categories:14R10, 14R20, 14R25, 13N15 
