Derivations Of Triangular Algebras Research Articles

Characterizations of Lie-type derivations of triangular algebras with local actions

Characterizations of Lie-type derivations of triangular algebras with local actions

Ternary mappings of triangular algebras

We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.

Lie derivations of triangular algebras without assuming unity

ABSTRACT In this paper we initiate the study of mapping problems on triangular algebras without assuming unity. We give the definitions of strong faithful bimodules, extreme centres, and extreme Lie derivations. Our main result is to give a description of Lie derivations on triangular algebras without assuming unity. As an application we shall give a characterization of Lie derivations on upper triangular matrix algebras over a faithful algebra.

A note on Jordan -derivations of triangular algebras

The aim of the paper is to prove that every Jordan -derivation of a triangular algebra that exists either a left weak loyal bimodule or a right weak loyal bimodule, is a -derivation. As an application we show that every Jordan -derivation of a (block) upper triangular matrix algebra, where , is a -derivation, which improves some results given by Benkovič in 2016.

Zero-Sum Coefficient Derivations in Three Variables of Triangular Algebras

Under mild assumptions Benkovi\v{c} showed that an $f$-derivation of a triangular algebra is a derivation when the sum of the coefficients of the multilinear polynomial $f$ is nonzero. We investigate the structure of $f$-derivations of triangular algebras when $f$ is of degree 3 and the coefficient sum is zero. The zero-sum coeffient derivations include Lie derivations (degree 2) and Lie triple derivations (degree 3), which have been previously shown to be not necessarily derivations but in standard form, i.e., the sum of a derivation and a central map. In this paper, we present sufficient conditions on the coefficients of $f$ to ensure that any $f$-derivations are derivations or are in standard form.<br /><br />

Jordan σ-derivations of triangular algebras

We consider the problem of describing the form Jordan -derivations of a triangular algebra . The main result states that every Jordan -derivation of is of the form , where is a -derivation of and is a special mapping of . We search for sufficient conditions on a triangular algebra, such that . In particular, any Jordan -derivation of a nest algebra is a -derivation and any Jordan -derivation of an upper triangular matrix algebra , where is a commutative unital algebra, is a -derivation.

Nonlinear Jordan Triple Derivations of Triangular Algebras

In this paper, it is proved that every nonlinear Jordan triple derivation on triangular algebra is an additive derivation.