Abstract
Consider a Lie color algebra, denoted by L. Our aim in this paper is to study the Lie triple derivations TDer(L) and generalized Lie triple derivations GTDer(L) of Lie color algebras. We discuss the centroids, quasi centroids and central triple derivations of Lie color algebras, where we show the relationship of triple centroids, triple quasi centroids and central triple derivation with Lie triple derivations and generalized Lie triple derivations of Lie color algebras L. A classification of Lie triple derivations algebra of all perfect Lie color algebras is given, where we prove that for a perfect and centerless Lie color algebra, TDer(L)=Der(L) and TDer(Der(L))=Inn(Der(L)).
Highlights
Researchers have worked on the concept of derivations, generalized derivations, centroids and quasi centroids with different perspectives in [11,12,13,14]
We focus on the Lie triple derivations, which are first introduced by Müller [15]
For perfect Lie color algebra
Summary
Researchers have worked on the concept of derivations, generalized derivations, centroids and quasi centroids with different perspectives in [11,12,13,14]. Wang and Xiao [16] studied the Lie triple derivations of incidence algebras, which is a type of operator algebra. Lie triple derivations GTDer (L)) of a Lie color algebra L. We discuss centroids and quasi centroids of Lie color algebras and evaluate some important results. Result consists in the complete classification of Lie triple derivations of a Lie color algebra. We obtain the relation of centroid and quasi centroid with Lie triple derivations (generalized Lie triple derivations) of Lie color algebra L.
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