1. CJM Online first
 Ghahramani, F.; Zadeh, S.

Bipositive isomorphisms between Beurling algebras and between their second dual algebras
Let $G$ be a locally compact group and let $\omega$ be a continuous
weight on $G$. We show that for each of the Banach algebras $L^1(G,\omega)$,
$M(G,\omega)$, $LUC(G,\omega^{1})^*$ and $L^1(G,\omega)^{**}$,
the order structure combined with the algebra structure determines
the weighted group.
Keywords:locally compact group, Beurling algebra, Arens product, topological group isomorphism, bipositive algebra isomorphism Categories:43A20, 43A22 

2. CJM Online first
 Fischer, Vera; Mejia, Diego Alejandro

Splitting, Bounding, and Almost Disjointness can be quite Different
We prove the consistency of
$$
\operatorname{add}(\mathcal{N})\lt
\operatorname{cov}(\mathcal{N})
\lt \mathfrak{p}=\mathfrak{s}
=\mathfrak{g}\lt \operatorname{add}(\mathcal{M})
= \operatorname{cof}(\mathcal{M}) \lt \mathfrak{a}
=\mathfrak{r}=\operatorname{non}(\mathcal{N})=\mathfrak{c}
$$
with $\mathrm{ZFC}$, where each of these cardinal
invariants assume arbitrary
uncountable regular values.
Keywords:cardinal characteristics of the continuum, splitting, bounding number, maximal almostdisjoint families, template forcing iterations, isomorphismofnames Categories:03E17, 03E35, 03E40 

3. CJM Online first
 Hartz, Michael

On the isomorphism problem for multiplier algebras of NevanlinnaPick spaces
We continue the investigation of the isomorphism problem for
multiplier algebras of reproducing kernel
Hilbert spaces with the complete NevanlinnaPick property.
In contrast to previous work in this area,
we do not study these spaces by identifying them with restrictions
of a universal space, namely the DruryArveson space.
Instead, we work directly with the Hilbert spaces and their
reproducing kernels. In particular,
we show that two multiplier algebras of NevanlinnaPick spaces
on the same set are equal if and only if the Hilbert
spaces are equal. Most of the article is devoted to the study
of a special class of
complete NevanlinnaPick spaces on homogeneous varieties. We
provide a complete
answer to the question of when two multiplier algebras of spaces
of this type
are algebraically or isometrically isomorphic. This generalizes
results of Davidson, Ramsey, Shalit,
and the author.
Keywords:nonselfadjoint operator algebras, reproducing kernel Hilbert spaces, multiplier algebra, NevanlinnaPick kernels, isomorphism problem Categories:47L30, 46E22, 47A13 

4. CJM 2015 (vol 68 pp. 44)
 Fernández Bretón, David J.

Strongly Summable Ultrafilters, Union Ultrafilters, and the Trivial Sums Property
We answer two questions of Hindman, SteprÄns and Strauss,
namely we prove that every
strongly summable
ultrafilter on an abelian group is sparse and has the trivial
sums property. Moreover we
show that in most
cases the sparseness of the given ultrafilter is a
consequence of its being isomorphic to a union ultrafilter. However,
this does not happen
in all cases:
we also construct (assuming Martin's Axiom for countable partial
orders, i.e.
$\operatorname{cov}(\mathcal{M})=\mathfrak c$), on the
Boolean group, a strongly summable ultrafilter that
is not additively isomorphic to any union ultrafilter.
Keywords:ultrafilter, StoneCech compactification, sparse ultrafilter, strongly summable ultrafilter, union ultrafilter, finite sum, additive isomorphism, trivial sums property, Boolean group, abelian group Categories:03E75, 54D35, 54D80, 05D10, 05A18, 20K99 

5. CJM 1999 (vol 51 pp. 49)
 Ndombol, Bitjong; El haouari, M.

AlgÃ¨bres quasicommutatives et carrÃ©s de Steenrod
Soit $k$ un corps de caract\'eristique $p$ quelconque. Nous
d\'efinissons la cat\'egorie des $k$alg\`ebres de cocha\^{\i}nes
fortement quasicommutatives et nous donnons une condition
n\'ecessaire et suffisante pour que l'alg\`ebre de cohomologie \`a
coefficients dans $\mathbb{Z}_2$ d'un objet de cette cat\'egorie soit
un module instable sur l'alg\`ebre de Steenrod \`a coefficients dans
$\mathbb{Z}_2$.
A tout c.w.\ complexe simplement connexe de type fini $X$ on associe une
$k$alg\`ebre de cocha\^{\i}nes fortement quasicommutative; la
structure de module sur l'alg\`ebre de Steenrod d\'efinie sur
l'alg\`ebre de cohomologie de celleci co\"\i ncide avec celle de
$H^*(X; \mathbb{Z}_2)$.
We define the category of strongly quasicommutative cochain
$k$algebras, where $k$ is a field of any characteristic $p$. We give a
necessary and sufficient condition which enables the cohomology algebra
with $\mathbb{Z}_2$coefficients of an object in this category
to be an unstable module on the $\mathbb{Z}_2$Steenrod algebra.
To each simply connected c.w.\ complex of finite type $X$ is associated
a strongly quasicommutative model and the module structure over the
$\mathbb{Z}_2$Steenrod algebra defined on the cohomology of
this model is the usual structure on $H^*(X; \mathbb{Z}_2)$.
Keywords:algÃ¨bres de cocha\^{\i}nes (fortement) quasicommutatives, $T (V)$modÃ¨le, carrÃ©s de Steenrod, quasiisomorphisme Categories:55P62, 55S05 

6. CJM 1998 (vol 50 pp. 210)
 Zhao, Kaiming

Isomorphisms between generalized Cartan type $W$ Lie algebras in characteristic $0$
In this paper, we determine when two simple generalized Cartan
type $W$ Lie algebras $W_d (A, T, \varphi)$ are isomorphic, and discuss
the relationship between the Jacobian conjecture and the generalized
Cartan type $W$ Lie algebras.
Keywords:Simple Lie algebras, the general Lie algebra, generalized Cartan type $W$ Lie algebras, isomorphism, Jacobian conjecture Categories:17B40, 17B65, 17B56, 17B68 
