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1. 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 almost-disjoint families, template forcing iterations, isomorphism-of-namesCategories:03E17, 03E35, 03E40

2. CJM Online first

Hartz, Michael
 On the isomorphism problem for multiplier algebras of Nevanlinna-Pick spaces We continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick 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 Drury-Arveson space. Instead, we work directly with the Hilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna-Pick 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 Nevanlinna-Pick 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:non-selfadjoint operator algebras, reproducing kernel Hilbert spaces, multiplier algebra, Nevanlinna-Pick kernels, isomorphism problemCategories:47L30, 46E22, 47A13

3. 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, SteprÄns 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, Stone-Cech compactification, sparse ultrafilter, strongly summable ultrafilter, union ultrafilter, finite sum, additive isomorphism, trivial sums property, Boolean group, abelian groupCategories:03E75, 54D35, 54D80, 05D10, 05A18, 20K99

4. CJM 1999 (vol 51 pp. 49)

Ndombol, Bitjong; El haouari, M.
 AlgÃ¨bres quasi-commutatives 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 quasi-commutatives 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 quasi-commutative; la structure de module sur l'alg\ebre de Steenrod d\'efinie sur l'alg\ebre de cohomologie de celle-ci co\"\i ncide avec celle de $H^*(X; \mathbb{Z}_2)$. We define the category of strongly quasi-commutative 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 quasi-commutative 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) quasi-commutatives, $T (V)$-modÃ¨le, carrÃ©s de Steenrod, quasi-isomorphismeCategories:55P62, 55S05

5. 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 conjectureCategories:17B40, 17B65, 17B56, 17B68
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