1. CJM Online first
 Elduque, Alberto

Order $3$ elements in $G_2$ and idempotents in symmetric composition algebras
Order three elements in the exceptional groups of type $G_2$
are classified up to conjugation over arbitrary fields. Their
centralizers are computed, and the associated classification
of idempotents in symmetric composition algebras is obtained.
Idempotents have played a key role in the study and classification
of these algebras.
Over an algebraically closed field, there are two conjugacy classes
of order three elements in $G_2$ in characteristic not $3$ and
four of them in characteristic $3$. The centralizers in characteristic
$3$ fail to be smooth for one of these classes.
Keywords:symmetric composition algebra, Okubo algebra, automorphism group, centralizer, idempotent Categories:17A75, 14L15, 17B25, 20G15 

2. CJM Online first
3. CJM 2014 (vol 67 pp. 286)
 Bell, Jason P.; Lagarias, Jeffrey C.

A SkolemMahlerLech Theorem for Iterated Automorphisms of $K$algebras
This paper proves a commutative algebraic extension
of a generalized SkolemMahlerLech theorem due to the first
author.
Let $A$ be a finitely generated commutative $K$algebra
over a field of characteristic $0$, and let $\sigma$ be
a $K$algebra automorphism of $A$.
Given ideals $I$ and $J$ of $A$, we show that
the set $S$ of integers $m$ such that
$\sigma^m(I) \supseteq J$ is a finite union of
complete doubly infinite arithmetic progressions in $m$, up to
the addition of a finite set.
Alternatively, this result states that for an affine scheme
$X$ of finite type over $K$,
an automorphism $\sigma \in \operatorname{Aut}_K(X)$, and $Y$ and $Z$
any two closed subschemes of $X$, the set
of integers $m$ with $\sigma^m(Z ) \subseteq Y$ is as above.
The paper presents examples
showing that this result may fail to hold if the affine scheme
$X$ is
not of finite type, or if $X$ is of finite type but the field
$K$ has positive characteristic.
Keywords:automorphisms, endomorphisms, affine space, commutative algebras, SkolemMahlerLech theorem Categories:11D45, 14R10, 11Y55, 11D88 

4. CJM 2011 (vol 64 pp. 1075)
 Raja, Chandiraraj Robinson Edward

A Stochastic Difference Equation with Stationary Noise on Groups
We consider the stochastic difference equation $$\eta _k = \xi _k
\phi (\eta _{k1}), \quad k \in \mathbb Z $$ on a locally compact group $G$
where $\phi$ is an automorphism of $G$, $\xi _k$ are given $G$valued
random variables and $\eta _k$ are unknown $G$valued random variables.
This equation was considered by Tsirelson and Yor on
onedimensional torus. We consider the case when $\xi _k$ have a
common law $\mu$ and prove that if $G$ is a distal group and $\phi$
is a distal automorphism of $G$ and if the equation has a solution,
then extremal solutions of the equation are in oneone
correspondence with points on the coset space $K\backslash G$ for
some compact subgroup $K$ of $G$ such that $\mu$ is supported on
$Kz= z\phi (K)$ for any $z$ in the support of $\mu$. We also provide
a necessary and sufficient condition for the existence of solutions
to the equation.
Keywords:dissipating, distal automorphisms, probability measures, pointwise distal groups, shifted convolution powers Categories:60B15, 60G20 

5. CJM 2011 (vol 64 pp. 3)
 Boissière, Samuel

Automorphismes naturels de l'espace de Douady de points sur une surface
On Ã©tablit quelques rÃ©sultats gÃ©nÃ©raux relatifs Ã la taille
du groupe d'automorphismes de l'espace de Douady de points sur une
surface, puis on Ã©tudie quelques propriÃ©tÃ©s des automorphismes
provenant d'un automorphisme de la surface, en particulier leur action
sur la cohomologie et la classification de leurs points fixes.
Keywords:SchÃ©ma de Hilbert, automorphismes, points fixes Category:14C05 

6. CJM 2003 (vol 55 pp. 533)
 Edo, Eric

Automorphismes modÃ©rÃ©s de l'espace affine
Le probl\`eme de JungNagata ({\it cf.}\ [J], [N]) consiste \`a savoir
s'il existe des automorphismes de $k[x,y,z]$ qui ne sont pas
mod\'er\'es. Nous proposons une approche nouvelle de cette question,
fond\'ee sur l'utilisation de la th\'eorie des automates et du
polygone de Newton. Cette approche permet notamment de g\'en\'eraliser
de fa\c con significative les r\'esultats de [A].
The JungNagata's problem ({\it cf.}\ [J], [N]) asks if there exists
nontame (or wild) automorphisms of $k[x,y,z]$. We give a new way to
attack this question, based on the automata theory and the Newton
polygon. This new approch allows us to generalize significantly the
results of [A].
Keywords:tame automorphisms, automata, Newton polygon Category:14R10 

7. CJM 2001 (vol 53 pp. 631)
 Walters, Samuel G.

KTheory of NonCommutative Spheres Arising from the Fourier Automorphism
For a dense $G_\delta$ set of real parameters $\theta$ in $[0,1]$
(containing the rationals) it is shown that the group $K_0 (A_\theta
\rtimes_\sigma \mathbb{Z}_4)$ is isomorphic to $\mathbb{Z}^9$, where
$A_\theta$ is the rotation C*algebra generated by unitaries $U$, $V$
satisfying $VU = e^{2\pi i\theta} UV$ and $\sigma$ is the Fourier
automorphism of $A_\theta$ defined by $\sigma(U) = V$, $\sigma(V) =
U^{1}$. More precisely, an explicit basis for $K_0$ consisting of
nine canonical modules is given. (A slight generalization of this
result is also obtained for certain separable continuous fields of
unital C*algebras over $[0,1]$.) The Connes Chern character $\ch
\colon K_0 (A_\theta \rtimes_\sigma \mathbb{Z}_4) \to H^{\ev} (A_\theta
\rtimes_\sigma \mathbb{Z}_4)^*$ is shown to be injective for a dense
$G_\delta$ set of parameters $\theta$. The main computational tool in
this paper is a group homomorphism $\vtr \colon K_0 (A_\theta
\rtimes_\sigma \mathbb{Z}_4) \to \mathbb{R}^8 \times \mathbb{Z}$
obtained from the Connes Chern character by restricting the
functionals in its codomain to a certain ninedimensional subspace of
$H^{\ev} (A_\theta \rtimes_\sigma \mathbb{Z}_4)$. The range of $\vtr$
is fully determined for each $\theta$. (We conjecture that this
subspace is all of $H^{\ev}$.)
Keywords:C*algebras, Ktheory, automorphisms, rotation algebras, unbounded traces, Chern characters Categories:46L80, 46L40, 19K14 
