Related papers: Nijenhuis tensor and invariant polynomials

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…

We study Nijenhuis structures on Courant algebroids in terms of the canonical Poisson bracket on their symplectic realizations. We prove that the Nijenhuis torsion of a skew-symmetric endomorphism N of a Courant algebroid is skew-symmetric…

In this paper, we introduce right-invariant (similarly, left-invariant) Poisson-Nijenhuis Structures on Lie groupoids and their infinitesimal counterparts as called $(\Lambda , \mathbf{n})-$structures. We present a mutual correspondence…

We introduce the notion of pseudo-Poisson Nijenhuis manifolds. These manifolds are generalizations of Poisson Nijenhuis manifolds by Magri and Morosi \cite{MM}. We show that any pseudo-Poisson Nijenhuis manifold has an associated quasi-Lie…

We define the Poisson quasi-Nijenhuis structures with background on Lie algebroids and we prove that to any generalized complex structure on a Courant algebroid which is the double of a Lie algebroid is associated such a structure. We prove…

Though algebraic geometry over $\mathbb C$ is often used to describe the closure of the tensors of a given size and complex rank, this variety includes tensors of both smaller and larger rank. Here we focus on the $n\times n\times n$…

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…

Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…

We propose a definition of Poisson quasi-Nijenhuis Lie algebroids as a natural generalization of Poisson quasi-Nijenhuis manifolds and show that any such Lie algebroid has an associated quasi-Lie bialgebroid. Therefore, also an associated…

We study {\em right-invariant (resp., left-invariant) Poisson quasi-Nijenhuis structures} on a Lie group $G$ and introduce their infinitesimal counterpart, the so-called {\em r-qn structures} on the corresponding Lie algebra $\mathfrak g$.…

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…

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 this paper, we study invariants of second order tensors in an $n$-dimensional flat Riemannian space. We define eigenvalues, eigenvectors and characteristic polynomials for second order tensors in such an $n$-dimensional Riemannian space…

A ternary Nambu-Poisson algebra (which we call a Nambu-Poisson algebra in the paper) is the underlying algebraic structure of Nambu-Poisson manifolds of order $3$ that appeared in the generalized Hamiltonian mechanics. First, we consider…

We investigate Nijenhuis deformations of $L_\infty$-algebras, a notion that unifies several Nijenhuis deformations, namely those of Lie algebras, Lie algebroids, Poisson structures and Courant structures. Additional examples, linked to Lie…

We analyze the structure of the algebra N of symmetric polynomials in non-commuting variables in so far as it relates to its commutative counterpart. Using the "place-action" of the symmetric group, we are able to realize the latter as the…

We give a proof of the KAM theorem on the existence of invariant tori for weakly perturbed Hamiltonian systems, based on Thirring's approach for Hamiltonians that are quadratic in the action variables. The main point of this approach is…

We study almost complex structures with lower bounds on the rank of the Nijenhuis tensor. Namely, we show that they satisfy an $h$-principle. As a consequence, all parallelizable manifolds and all manifolds of dimension $2n\geq 10$…

This note aims to continue our study about the applications of Poisson quasi-Nijenhuis geometry to the theory of classical completely integrable systems. More precisely, we will present new versions of the deformation and involutivity…

We prove a general existence theorem for nonlinear partial differential systems of any order in one complex variable. A special case of first order contains a well-known theorem of Nijenhuis and Woolf concerning local existence of…