Related papers: Jordan chains of $h$-cyclic matrices

For any positive integer $n$, $n$-derived-simple derived discrete algebras are classified up to derived equivalence. Furthermore, the Jordan-H\"older theorems for all kinds of derived categories of derived discrete algebras are obtained.

Let $\mathcal{R}$ be a commutative ring with identity, $I(X,\mathcal{R})$ be the incidence algebra of a locally finite pre-ordered set $X$. In this note, we characterise the derivations of $I(X,\mathcal{R})$ and prove that every Jordan…

The aim of this article is to start a study of Jordan derivations in finite endomorphism semirings.

We elucidate the geometry of matrix models based on simple formally real Jordan algebras. Such Jordan algebras give rise to a nonassociative geometry that is a generalization of Lorentzian geometry. We emphasize constructions for the…

We consider partial and total reduction of a nonhomogeneous linear system of the operator equations with the system matrix in the same particular form as in paper [N. Shayanfar, M. Hadizadeh 2013]. Here we present two different concepts.…

We describe the structure of all continuous Jordan triple endomorphisms of the set $\mathbb{P}_2$ of all positive definite $2\times 2$ matrices thus completing a recent result of ours. We also mention an application concerning sorts of…

Let $G$ be a non-connected reductive algebraic group over an algebraically closed field $\mathbb{K}$ and let $D$ be a connected component of $G$. We investigate Jordan classes of $D$ and we obtain a description of the regular part of the…

A commutative loop is Jordan if it satisfies the identity $x^2 (y x) = (x^2 y) x$. Using an amalgam construction and its generalizations, we prove that a nonassociative Jordan loop of order $n$ exists if and only if $n\geq 6$ and $n\neq 9$.…

Roots of matrices are well-studied. The conditions for their existence are understood: The block sizes of nilpotent Jordan blocks, arranged in pairs, have to satisfy some simple algebraic property. More interesting are structured roots of…

We announce here a number of results concerning representation theory of the algebra $R=k<x,y>/ (xy-yx-y^2)$, known as Jordan plane (or Jordan algebra). We consider the question on 'classification' of finite-dimensional modules over the…

In the present paper we prove that every 2-local inner derivation on the Jordan ring of self-adjoint matrices over a commutative involutive ring is a derivation. We also apply our technique to various Jordan algebras of infinite dimensional…

We determine the composition factors of a Jordan-H\"older series including multiplicities of the locally analytic Steinberg representation. For this purpose we prove the acyclicity of the evaluated locally analytic Tits complex giving rise…

In this note, we prove that any Jordan derivation on the generalized matrix ring $T_n(R,M)$ is a derivation. This extends some well-known results of this branch due to Bre\v{s}ar et al. in the cited literature.

Let $R$ be a ring and $Z(R)$ be the center of $R.$ The aim of this paper is to define the notions of centrally extended Jordan derivations and centrally extended Jordan $\ast$-derivations, and to prove some results involving these mappings.…

In this paper, we calculate the Jordan decomposition (or say, the Jordan canonical form) for a class of non-symmetric Ornstein-Uhlenbeck operators with the drift coefficient matrix being a Jordan block and the diffusion coefficient matrix…

In this paper we prove that any nonlinear Jordan derivation on triangular algebras is an additive derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinite dimensional Hilbert spaces is inner.

Eventually positive matrices are real matrices whose powers become and remain strictly positive. As such, eventually positive matrices are a fortiori matrix roots of positive matrices, which motivates us to study the matrix roots of…

Let $\mathfrak{A}$ be a unital ring with a nontrivial idempotent. In this paper, it is shown that under certain conditions every multiplicative generalized Jordan $n$-derivation $\Delta:\mathfrak{A}\rightarrow\mathfrak{A}$ is additive. More…

We study the Jordan-Hoelder series for nearby cycles on certain Shimura varieties and Rapoport-Zink local models, and on finite-dimensional pieces of Beilinson's deformation of the affine Grassmannian to the affine flag variety (and their…

In this paper, we develop a method to obtain the algebraic classification of noncommutative Jordan algebras from the classification of Jordan algebras of the same dimension. We use this method to obtain the algebraic classification of…