Hom-Lie Algebras on Strictly Upper Triangular Matrices Lie Algebra Over a Commutative Ring: Derivation Case

Abstract

Let n be the nilpotent Lie algebra consisting of all strictly upper triangular n n × matrices over a commutative ring. In this paper, we characterize the decomposition of the derivations of n when ( ) φ , n is a hom-Lie algebra.Meanwhile, the isomorphic classes are also determined.