Related papers: A Le Page--Kaplansky theorem characterizing commut…

Let $\gamma = (\gamma_1,...,\gamma_N)$, $N \geq 2$, be a system of proper contractions on a complete metric space. Then there exists a unique self-similar non-empty compact subset $K$. We consider the union ${\mathcal G} = \cup_{i=1}^N…

We associate a non-commutative $C^*$-algebra with any locally finite simplicial complex. We determine the $K$-theory of these algebras and show that they can be used to obtain a conceptual explanation for the Baum-Connes conjecture.

We describe the one-dimensional \v{C}eby\v{s}\"{e}v subspaces of a JBW$^*$-triple $M,$ by showing that for a non-zero element $x$ in $M$, $\mathbb{C}x$ is a \v{C}eby\v{s}\"{e}v subspace of $M$ if, and only if, $x$ is a Brown-Pedersen…

We study new classes of linear preservers between C$^*$-algebras and JB$^*$-triples. Let $E$ and $F$ be JB$^*$-triples with $\partial_{e} (E_1)$. We prove that every linear map $T:E\to F$ strongly preserving Brown-Pedersen quasi-invertible…

Let G be a simple algebraic group over an algebraically closed field k of characteristic 2. We consider analogues of the Jacobson-Morozov theorem in this setting. More precisely, we classify those nilpotent elements with a simple…

In 1997, Kaplansky conjectured that if two positive definite ternary quadratic forms with integer coefficients have perfectly identical integral representations, then they are isometric, both regular, or included either of two families of…

The principal result in this note is a strengthened version of Kadison's transitivity theorem for unital JB$^*$-algebras, showing that for each minimal tripotent $e$ in the bidual, $\mathfrak{A}^{**}$, of a unital JB$^*$-algebra…

In this paper, we find a criterium for universal equivalence of partially commutative Lie algebras whose defining graphs are trees. Besides, we obtain bases for partially commutative metabelian Lie algebras.

We show that the predual of a JBW$^*$-triple has the weak Banach-Saks property, that is, reflexive subspaces of a JBW$^*$-triple predual are super-reflexive. We also prove that JBW$^*$-triple preduals satisfy the Koml\'os property (which…

We study the structure of a Leibniz triple system $\mathcal{E}$ graded by an arbitrary abelian group $G$ which is considered of arbitrary dimension and over an arbitrary base field $\mathbb{K}$. We show that $\mathcal{E}$ is of the form…

We consider modules E over a C*-algebra A which are equipped with a map into A_+ that has the formal properties of a norm. We completely determine the structure of these modules. In particular, we show that if A has no nonzero commutative…

We show that every separable simple tracially approximately divisible $C^*$-algebra has strict comparison, is either purely infinite, or has stable rank one. As a consequence, we show that every (non-unital) finite simple ${\cal Z}$-stable…

We say that a $C^*$-algebra $\mathcal{A}$ satisfies the similarity property ((SP)) if every bounded homomorphism $u\colon \mathcal{A} \to \mathcal{B}(\mathit{H})$, where $\mathit{H}$ is a Hilbert space, is similar to a $*$-homomorphism. We…

The famous Jacobian conjecture asks if a morphism $f:K[x,y]\to K[x,y]$ having an invertible Jacobian is invertible ($K$ is a characteristic zero field). We show that if one of the following three equivalent conditions is satisfied, then $f$…

We extend the Lee-Schiffler Dyck path model to give a proof of the Kontsevich non-commutative cluster positivity conjecture with unequal parameters.

A matching is indecomposable if it does not contain a nontrivial contiguous segment of vertices whose neighbors are entirely contained in the segment. We prove a Ramsey-like result for indecomposable matchings, showing that every…

In this article, we study the permanence of topological and algebraic dimension type properties of simple unital $C\sp*$-algebras. When a pair of unital $C\sp*$-algebras $(A, B)$ is associated by a $*$-homomorphism $\phi: A\to B$ which is…

We conduct a computability-theoretic study of Ramsey-like theorems of the form "Every coloring of the edges of an infinite clique admits an infinite sub-clique avoiding some pattern", with a particular focus on transitive patterns. As it…

The CBH theorem characterises quantum theory within a C*-algebraic framework. Namely, mathematical properties of C*-algebras modelling quantum systems are equivalent to constraints that are information-theoretic in nature: (1)…

We present a new and simple proof of a theorem due to Kaplansky which unifies theorems of Kolchin and Levitzki on triangularizability of semigroups of matrices. We also give two different extensions of the theorem. As a consequence, we…