Related papers: Szego and Widom Theorems for the Neil Algebra
We define the twisted loop Lie algebra of a finite dimensional Lie algebra $\mathfrak g$ as the Fr\'echet space of all twisted periodic smooth mappings from $\mathbb R$ to $\mathfrak g$. Here the Lie algebra operation is continuous. We call…
We show that the following two algebras are isomorphic. The first is the algebra $A_P$ of functions on the scheme of monic linear second-order differential operators on $\C$ with prescribed regular singular points at $z_1,..., z_n, \infty$,…
The study of derivations and their generalizations on non-associative algebras has proven to be fundamental in understanding the internal symmetries and algebraic dynamics of such structures. In this paper, we investigate derivations and…
The Grothendieck-Teichm\"uller Lie algebra is a Lie subalgebra of a Lie algebra of derivations of the free Lie algebra in two generators. We show that the lower central series of the latter Lie algebra induces a decreasing filtration of the…
Originating in the work of A.M. Semikhatov and D. Adamovi\'c, inverse reductions are embeddings involving W-algebras corresponding to the same Lie algebra but different nilpotent orbits. Here, we show that an inverse reduction embedding…
Let $\mathcal M$ be a factor von Neumann algebra with separable predual and let $T\in \mathcal M$. We call $T$ an irreducible operator (relative to $\mathcal M$) if $W^*(T)$ is an irreducible subfactor of $\mathcal M$, i.e., $W^*(T)'\cap…
Recently M.E. Shirokov introduced the non-commutative operator graph depending on the complex parameter $\theta $ to construct channels with positive quantum zero-error capacity having vanishing n-shot capacity. We study the algebraic…
Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…
Let $\operatorname{Witt}$ be the Lie algebra generated by the set $\{L_i\,\vert\, i \in {\mathbb Z}\}$ and $\operatorname{Vir}$ its universal central extension. Let $\operatorname{Diff}(V)$ be the Lie algebra of differential operators on…
The concepts of derivations and right derivations for Leibniz algebras and $K$-B quasi-Jordan algebras naturally arise from the inner derivations determined by their algebraic structures. In this paper we introduce the corresponding…
It is proved an inequality - integrated analogue of the Hardy inequality and as application simplified proof of the theorem of S. A. Vinogradov for the bounded Toeplitz operators on the space of functions analytic and bounded in the unit…
Let $E$ be the open unit disk $\{z\in \mathbb{C}: |z|<1\}$. Let $A$ be the class of analytic functions in $E$, which have the form $f(z)=z+a_2z^2+...$. We define operators $L_n^\sigma\colon A\to A$ using the convolution *. Using these…
The induction and reduction precesses of an O*-vector space $\M$ obtained by means of a projection taken, respectively, in $\M$ itself or in its weak bounded commutant $\M'_\w$ are studied. In the case where $\M$ is a partial GW*-algebra,…
We consider a class of weighted harmonic functions in the open upper half-plane known as $\alpha$-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the…
We introduce a new example of unital commutative $n$-dimensional group algebra $\mathbb{R}_n$ for $n \geq 2$. The algebra $\mathbb{R}_n$ and the complex numbers $\mathbb{C}$ are astonishingly alike. The zero divisor set of the algebra has…
Based on operators borrowed from scattering theory, several concrete realizations of index theorems are proposed. The corresponding operators belong to some C*-algebras of pseudo-differential operators with coefficients which either have…
Families of vertex algebras associated to nilpotent elements of simply-laced Lie algebras are constructed. These algebras are close cousins of logarithmic W-algebras of Feigin and Tipunin and they are also obtained as modifications of…
We classify anti-involutions of Lie superalgebra $\hsd$ preserving the principal gradation, where $\hsd$ is the central extension of the Lie superalgebra of differential operators on the super circle $S^{1|1}$. We clarify the relations…
For a family of Jacobians of smooth pointed curves there is a notion of tautological algebra. There is an action of $\mathfrak{sl}_2$ on this algebra. We define and study a lifting of the Polishchuk operator, corresponding to $f\in…
In a previous paper we showed how the main theorems characterizing operator algebras and operator modules, fit neatly into the framework of the `noncommutative Shilov boundary', and more particularly via the left multiplier operator algebra…