Related papers: Rota-type operators on 2-dimensional dendriform al…
A class of well-behaved *-representations of a q-deformed Heisenberg algebra is studied and classified.
We introduce the concept of an extended O-operator that generalizes the well-known concept of a Rota-Baxter operator. We study the associative products coming from these operators and establish the relationship between extended O-operators…
Theory of Rota-Baxter operators on rings and algebras has been developed since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined the notion of Rota-Baxter operator on a group. We provide some general constructions of…
This paper studies the Nijenhuis operator on Hom-Leibniz conformal algebra, defining their representations and cohomologies. We determine the cohomologies for both Hom-Leibniz conformal algebra and Nijenhuis operators on Hom-Leibniz…
Rota-Baxter systems were introduced by Brzezi\'{n}ski as a generalization of Rota-Baxter operators that are related to dendriform structures, associative Yang-Baxter pairs and covariant bialgebras. In this paper, we define Rota-Baxter…
The notion of matching Rota-Baxter algebras was recently introduced by Gao, Guo and Zhang [{\em J. Algebra} 552 (2020) 134-170] motivated by the study of algebraic renormalization of regularity structures. The concept of matching…
In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant.…
We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and…
A Rota-Baxter operator of weight $\lambda$ is an abstraction of both the integral operator (when $\lambda=0$) and the summation operator (when $\lambda=1$). We similarly define a differential operator of weight $\lambda$ that includes both…
Let K be a field of characteristic zero, and let m=(x_1,...,x_n)) be a maximal ideal of the polynomial ring K[x_1,...,x_n]. We classify all Rota--Baxter operators of weights zero and one on the truncated polynomial algebra…
Several spectra of analytically Riesz operators will be characterized. These results will led to prove Weyl and Browder type theorems for the aforementioned class of operators.
Presented is a free boson representation of the type II vertex operators for the $A_{n-1}^{(1)}$ face model. Using the bosonization, we derive some properties of the type II vertex operators, such as commutation, inversion and duality…
The article is devoted to the investigation of operators on a non locally compact group algebra. Their isomorphisms are also studied.
In this article, we characterize the radial operators on weighted Bergman spaces of Reinhardt domains in $\mathbb{C}^n$, the Dirichlet and the Hardy spaces of the open unit disk $\mathbb{D}$, in terms of integral representations. We also…
The theory of generalized Nijenhuis torsions, which extends the classical notions due to Nijenhuis and Haantjes, offers new tools for the study of normal forms of operator fields. We propose a general result ensuring that, given a family of…
There is a relatively well-known description of the algebra of (higher order) left differential operators on commutative algebras. This note gives a construction of similar flavor for algebras of differential operators on not necessarily…
This article explores Rota-Baxter operators on finite-dimensional $\omega$-Lie algebras over a field of characteristic not 2. We provide several methods for constructing left-symmetric algebras, $\omega$-Lie algebras, and Hom-Lie algebras…
The paper is devoted to the study of Nijenhuis operators of arbitrary dimension $n$ in a neighborhood of a point at which the first $n-1$ coefficients of the characteristic polynomial are functionally independent, and the last coefficient…
In terms of Nijenhuis geometry, left-symmetric algebras are the same as Nijenhuis operators whose entries are linear in coordinates. Here we consider Nijenhuis operators for which the coefficients of its characteristic polynomial are…
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital…