Related papers: Between Maharam's and von Neumann's problems

In this paper some results on the Lie structure of prime superalgebras are discussed. We prove that, with the exception of some special cases, for a prime superalgebra, $A$, over a ring of scalars $\Phi$ with $1/2\in \Phi$, if $L$ is a Lie…

Based on Bergman's Lemma on centralizers, we obtain a sharp lower degree bound for nonconstant elements in a subalgebra generated by two elements of a free associative algebra over an arbitrary field.

In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by…

We investigate the minimal number of generators $\mu$ and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the…

We prove that it is not possible to classify separable von Neumann factors of types $\II_1$, $\II_\infty$ or $\III_\lambda$, $0\leq \lambda\leq1$, up to isomorphism by a Borel measurable assignment of "countable structures" as invariants.…

The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…

In this work we study Leibniz algebras whose second-maximal subalgebras are ideals. We provide a classification based on solvability, nilpotency, and the size of the derived algebra. We give specific descriptions of those Leibniz algebras…

An arithmetic matroid is weakly multiplicative if the multiplicity of at least one of its bases is equal to the product of the multiplicities of its elements. We show that if such an arithmetic matroid can be represented by an integer…

Let ${\bf x}=(x_n)_n$ be a sequence in a Banach space. A set $A\subseteq \mathbb{N}$ is perfectly bounded, if there is $M$ such that $\|\sum_{n\in F}x_n\|\leq M$ for every finite $F\subseteq A$. The collection $B({\bf x})$ of all perfectly…

We develop the duality theory between ideals of multilinear operators and tensor norms that arises from the geometric approach of $\Sigma$-operators. To this end, we introduce and develop the notions of $\Sigma$-ideals of multilinear…

Assume that there is no quasi-measurable cardinal smaller than $2^\omega$. ($\kappa$ is quasi measurable if there exists $\kappa $-additive ideal $\ci $ of subsets of $\kappa $ such that the Boolean algebra $P(\kappa)/\ci$ satisfies c.c.c.)…

Let $n\geq 2$ and $G_n=\mathbb{Z}^n\rtimes SL_n(\mathbb{Z})$. We classify all $G_n$-invariant von Neumann subalgebras in $L(G_n)$. For $n=2$, this gives an alternative proof of the previous result of Jiang-Liu. For $n\geq 3$, this gives the…

With every $\sigma$-ideal $I$ on a Polish space we associate the $\sigma$-ideal $I^*$ generated by the closed sets in $I$. We study the forcing notions of Borel sets modulo the respective $\sigma$-ideals $I$ and $I^*$ and find connections…

A seminorm with square property on a real associative algebra is submultiplicative

We introduce algebras which are inductive limits of Banach spaces and carry inequalities which are counterparts of the inequality for the norm in a Banach algebra. We then define an associated Wiener algebra, and prove the corresponding…

Let $M$ be a von Neumann algebra with a faithful normal finite trace $t$, and $H^\infty$ be a finite, maximal, subdiagonal of $M$. Fundamental theorems on conjugate functions for weak* Dirichlet algebras are shown to be a bounded linear map…

Given an ideal $\mathcal{I}$ on the nonnegative integers $\omega$ and a Polish space $X$, let $\mathscr{L}(\mathcal{I})$ be the family of subsets $S\subseteq X$ such that $S$ is the set of $\mathcal{I}$-limit points of some sequence taking…

A {\it weak selection} on $\mathbb{R}$ is a function $f: [\mathbb{R}]^2 \to \mathbb{R}$ such that $f(\{x,y\}) \in \{x,y\}$ for each $\{x,y\} \in [\mathbb{R}]^2$. In this article, we continue with the study (which was initiated in \cite{ag})…

We characterize, in a purely algebraic manner, certain linear forms, called stable, on a Lie algebra. As an application, we determine the index of a Borel subalgebra of a semi-simple Lie algebra. Finally, we give an example of a parabolic…

We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having fixed class of nilpotence.