相关论文: On the Linearization of Certain Singularities of N…
A field of endomorphisms $R$ is called a Nijenhuis operator if its Nijenhuis torsion vanishes. In this work we study a specific kind of singular points of $R$ called points of scalar type. We show that the tangent space at such points…
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 aim of this paper is to classify all real and complex 3-dimensional Lie algebras admitting regular semisimple algebraic Nijenhuis operators. This problem is completely solved (see Theorems 2 and 3) by describing all Nijenhuis eigenbases…
A Nijenhuis operator $L$ is a $(1,1)$-tensor field on a smooth manifold $M$ with vanishing Nijenhuis torsion ${ {\mathcal N_L}}$. At each point $x\in M$, the algebraic type of $L(x)$ is characterized by its Jordan normal form. In this…
In this paper, we describe all Nijenhuis operators on 2-dimensional complex pre-Lie algebras and 3-dimensional complex associative algebras. As an application, using these operators, we obtain solutions of the classical Yang-Baxter equation…
In this paper, we study Nijenhuis operators on Leibniz algebras. We discuss the relationship of Nijenhuis operators with Rota-Baxter operators and modified Rota-Baxter operators on Leibniz algebras. We define a representation theory of…
The aim of this work is to introduce representations of BiHom-left-symmetric algebras. and develop its cohomology theory. As applications, we study linear deformations of BiHom-left-symmetric algebras, which are characterized by its second…
We study Nijenhuis operators, that is, (1,1)-tensors with vanishing Nijenhuis torsion under the additional assumption that they are gl-regular, i.e., every eigenvalue has geometric multiplicity one. We prove the existence of a coordinate…
In the paper, three-dimensional Nijenhuis operators are studied that have differential singularities, i.e., such points at which the coefficients of the characteristic polynomials are dependent. The case is studied in which the…
This work is the first, and main, of the series of papers in progress dedicated to Nienhuis operators, i.e., fields of endomorphisms with vanishing Nijenhuis tensor. It serves as an introduction to Nijenhuis Geometry that should be…
In this paper, we study $(n-1)$-order deformations of an $n$-Lie algebra and introduce the notion of a Nijenhuis operator on an $n$-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a Nijenhuis…
In this paper, we introduce compatible ternary Leibniz algebras, (dual)Nijenhuis pairs from the second-order deformation of ternary Leibniz algebras with a representarion and study the invariance of certains operators (generalized…
The core object of this paper is a pair $(L, e)$, where $L$ is a Nijenhuis operator and $e$ is a vector field satisfying a specific Lie derivative condition, i.e., $Lie_{e}L=\operatorname{Id}$. Our research unfolds in two parts. In the…
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…
The aim of this paper is twofold. In the first part, we define the cohomology of a Nijenhuis Lie algebra with coefficients in a suitable representation. Our cohomology of a Nijenhuis Lie algebra governs the simultaneous deformations of the…
The paper contains two lines of results: the first one is a study of symmetries and conservation laws of gl-regular Nijenhuis operators. We prove the splitting Theorem for symmetries and conservation laws of Nijenhuis operators, show that…
We investigate $\rho$-orthogonality and its local symmetry in the space of bounded linear operators. A characterization of Hilbert space operators with symmetric numerical range is established in terms of $\rho$-orthogonality. Further, we…
The purpose of this paper is to introduce an algebraic cohomology theory of left pre-Jacobi-Jordan algebras. We use the cohomological approach to study linear deformations of these algebras. We also introduce the notion of Nijenhuis…
In this paper, we introduce the cohomology theory of relative Rota-Baxter operators on Leibniz algebras. We use the cohomological approach to study linear and formal deformations of relative Rota-Baxter operators. In particular, the notion…
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…