Related papers: Nonlinear Jordan Derivations of Triangular Algebra…
Let $n\in \Bbb N,$ and let $A,B$ be two rings. An additive map $h: A\to B$ is called n-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $a \in {A}$. Every Jordan homomorphism is an n-Jordan homomorphism, for all $n\geq 2,$ but the converse…
Jordan isomorphisms of rings are defined by two equations. The first one is the equation of additivity while the second one concerns multiplicativity with respect to the so-called Jordan product. In this paper we present results showing…
We described $\delta$-derivations and $\delta$-superderivations of simple Jordan superalgebra <<KKM Double>> (also known as superalgebra of Jordan brackets) and unital simple finite-dimensional Jordan superalgebras over algebraic closed…
In this paper we investigate in details derivations on trivial extension algebras. We obtain generalizations of both known results on derivations on triangular matrix algebras and a known result on first cohomology group of trivial…
We study a class of matrix function algebras, here denoted $\mathcal{T}^{+}(\mathcal{C}_n)$. We introduce a notion of point derivations, and classify the point derivations for certain finite dimensional representations of…
A noncommutative Jordan algebra of a specific type is attached to any (-1,-1)-balanced Freudenthal Kantor triple system, in such a way that the triple product in this system is determined by the binary product in the algebra. Over fields of…
This study focuses on the analysis of derivations, centroids, and inner derivations of 5-dimensional complex nilpotent associative algebras. It presents the classification of these algebras of dimension less than five, as well as the…
The Jordan type of an Artinian algebra is the Jordan block partition associated to multiplication by a generic element of the maximal ideal. We study the Jordan type for Artinian Gorenstein (AG) local algebras A, and the interaction of…
Let $P$ be a preordered set, $R$ a ring and $FI(P,R)$ the finitary incidence ring of $P$ over $R$. We find a criterion for all Jordan derivations of $FI(P,R)$ to be derivations and generalize Theorem 3.3 from arXiv:1411.6123. In particular,…
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 work, we investigate anti-derivations and biderivation of Leibniz algebras. We describe general form of anti-derivations and biderivations on null-filiform and filiform Leibniz algebras. Moreover, we show how to construct Leibniz…
We prove that a Jordan $\calc^1$-curve in the plane contains any non-flat triangle up to translation and homothety with positive ratio. This is false if the curve is not $C^1$. The proof uses a bit configuration spaces, differential and…
We prove a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces.
In this paper, we define some new notions of triangular Banach algebras and we investigate the derivations on these algebras.
The aim of this paper is to show that between standard operator algebras every bijective map with a certain multiplicativity property related to Jordan triple isomorphisms of associative rings is automatically additive.
The concepts of derivations and right derivations for Leibniz algebras and $K$-B quasi-Jordan algebras naturally arise from the inner derivations determined by their algebraic structures. In this paper we introduce the corresponding…
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.
A basic problem for any class of nonassociative algebras is to determine the polynomial identities satisfied by the symmetrization and the skew-symmetrization of the original product. We consider the symmetrization of the product in the…
For any finite-dimensional Lie algebra we introduce the notion of Jordan-Kronecker invariants, study their properties and discuss examples. These invariants naturally appear in the framework of the bi-Hamiltonian approach to integrable…
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…