Related papers: Remarks on Jordan derivations over matrix algebras

We study finite-dimensional commutative algebras, which satisfy the Jacobi identity. Such algebras are Jordan algebras. We describe some of their properties and give a classification in dimensions $n<7$ over algebraically closed fields of…

The aim of this article is to introduce the concept of centrally-extended Jordan endomorphisms and proving that if $R$ is a non-commutative prime ring of characteristic not two, and $G$ is a CE- Jordan epimorphism such that $[G(x), x] \in…

We prove that every bounded local triple derivation on a unital C*-algebra is a triple derivation. A similar statement is established in the category of unital JB*-algebras.

In this paper, we compute all possible Jordan types of linear forms $\ell$ in any full Perazzo algebra $A$. In some cases we are also able to compute the corresponding Jordan degree type, which is a finer invariant.

The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…

With this paper we start a programme aiming at connecting two vast scientific areas: Jordan algebras and representation theory. Within representation theory, we focus on non-compact, real forms of semisimple Lie algebras and groups as well…

To each projection $p$ in a $C^*$-algebra $A$ we associate a family of derivations on $A$, called $p$-derivations, and relate them to the space of triple derivations on $p A (1-p)$. We then show that every derivation on a ternary ring of…

Determining the Jordan canonical form of the tensor product of Jordan blocks has many applications including to the representation theory of algebraic groups, and to tilting modules. Although there are several algorithms for computing this…

R.V. Kadison defined the notion of local derivation on an algebra and proved that every continuous local derivation on a von Neumann algebra is a derivation (Kadison 1990). We provide the analogous result in the setting of Jordan triples.

A century ago, Camille Jordan proved that the complex general linear group $GL_n(C)$ has the Jordan property: there is a Jordan constant $C_n$ such that every finite subgroup $H \le GL_n(C)$ has an abelian subgroup $H_1$ of index $[H : H_1]…

Let $X$ be a partially ordered set, $R$ a commutative $2$-torsionfree unital ring and $FI(X,R)$ the finitary incidence algebra of $X$ over $R$. In this note we prove that each $R$-linear Jordan isomorphism of $FI(X,R)$ onto an $R$-algebra…

For a C*-algebra A, G. Pedersen defined the concept of universal measurability for self-adjoint elements of A**, the universal enveloping algebra of A. Although he was unable to show that U, the set of universally measurable elements, is a…

In the present paper 2-local derivations on various algebras of infinite dimensional matrix-valued functions on a compact are considered. It is proved that every 2-local derivation on such algebra is a derivation. Also we explain that the…

Let $\Gamma$ be a connected graph without loops, cycles or multiple edges and $Z(\Gamma)$ the corresponding zigzag algebra. Then every Jordan derivation of $Z(\Gamma)$ is a derivation. Moreover, we will prove that the dimension of 1th…

Let $\mathcal{A}$ be a unital algebra, $\delta$ be a linear mapping from $\mathcal{A}$ into itself and $m$, $n$ be fixed integers. We call $\delta$ an (\textit{m, n})-derivable mapping at $Z$, if…

In this paper we consider the algebra of upper triangular matrices UT$_n(F)$, endowed with a $\mathbb{Z}_2$-grading (superalgebra) and equipped with a superinvolution. These structures naturally arise in the context of Lie and Jordan…

We describe all finite connected 3-transposition groups whose Matsuo algebras have nontrivial factors that are Jordan algebras. As a corollary, we show that if F is a field of characteristic 0, then there exist infinitely many primitive…

We study Jordan types of linear forms for graded Artinian Gorenstein algebras having arbitrary codimension. We introduce rank matrices of linear forms for such algebras that represent the ranks of multiplication maps in various degrees. We…

There are Jordan analogues of annihilators in Jordan algebras which are called Jordan annihilators. The present paper is devoted to investigation of those Jordan algebras every Jordan annihilator of which is generated by an idempotent as an…

The Jacobson Coordinatization Theorem describes the structure of unitary Jordan algebras containing the algebra $H_n(F)$ of symmetric nxn matrices over a field F with the same identity element, for $n\geq 3$. In this paper we extend the…