Related papers: On Indecomposable triples associated with nilpoten…

We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue of the Bercovici-Pata…

In this note we give a complete classification of all indecomposable yet reducible representations of $B_3$ for dimensions $2$ and $3$ over an algebraically closed field $K$ with characteristic $0$, up to equivalence. We illustrate their…

Let U(L) be the enveloping algebra of a finite dimensional Lie algebra L over a field k of characteristic zero, Z(U(L)) its center and Sz(U(L)) its semicenter. A sufficient condition is given in order for Sz(U(L)) to be a polynomial algebra…

Let $\mathcal M$ be a separable factor. An operator $T$ in $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann algebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e.,…

In this paper, continuous binary operations of a topological space are studied and a criterion of their invertibility is proved. The classification problem of groups of invertible continuous binary operations of locally compact and locally…

We classify the irreducible components of the varieties V(n,a,b) of pairs (A,B) of matrices of size n such that AB = BA = 0 and A^a = B^b = 0.

We give a condition ensuring that the operators in a nilpotent Lie algebra of linear operators on a finite dimensional vector space have a common eigenvector.

Let V be a finite dimensional complex superspace and G a simple (or a ``close'' to simple) Lie superalgebra of matrix type, i.e., a Lie subsuperalgebra in GL(V). Under the classical invariant theory for G we mean the description of…

Let $\N_n$ be the set of nilpotent $n$ by $n$ matrices over an algebraically closed field $k$. For each $r\ge 2$, let $C_r(\N_n)$ be the variety consisting of all pairwise commuting $r$-tuples of nilpotent matrices. It is well-kown that…

We study separability properties in a 5-dimensional set of states of quantum systems composed of three subsystems of equal but arbitrary finite Hilbert space dimension d. These are the states, which can be written as linear combinations of…

A classical theorem of von Neumann asserts that every unbounded self-adjoint operator $A$ in a separable Hilbert space $H$ is unitarily equivalent to an operator $B$ in $H$ such that $D(A)\cap D(B)=\{0\}$. Equivalently this can be…

The paper extends three results regarding the nth root problem by embedding classes of Hilbert-space operators into the class of posinormal operators. For instance, it is shown that (i) for coposinormal operators, if T is paranormal and T^n…

We study indecomposable representations of quivers on separable infinite-dimensional Hilbert spaces by bounded operators. We consider a complement of Gabriel's theorem for these representations. Let $\Gamma$ be a finite, connected quiver.…

In this paper, we classify (n+5)-dimensional nilpotent n-Lie algebras of class two over the arbitrary field, when $n\ge 3$.

We study, in the setting of algebraic varieties, finite-dimensional spaces of functions V that are invariant under a ring D^V of differential operators, and give conditions under which D^V acts irreducibly. We show how this problem,…

For a power bounded or polynomially bounded operator $T$ sufficient conditions for the existence of a nontrivial hyperinvariant subspace are given. The obtained hyperinvariant subspaces of $T$ have the form of the closure of the range of…

In this paper, we are concerned with conditions under which $[p(T)]^*=\bar{p}(T^*)$, where $p(z)$ is a one-variable complex polynomial, and $T$ is an unbounded, densely defined, and linear operator. Then, we deal with the validity of the…

This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent Novikov algebras.

We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topological characterization of indecomposability which is new even in…

The dimension of any module over an algebra of affiliated operators ${\mathcal U}$ of a finite von Neumann algebra ${\mathcal A}$ is defined using a trace on ${\mathcal A}.$ All zero-dimensional ${\mathcal U}$-modules constitute the torsion…