On Endomorphs of Right-Symmetric Algebras

Abstract

We introduce the notion of endomorph $E({\mathcal{A}})$ of a $($super$)$algebra ${\mathcal{A}}$ and prove that $E({\mathcal{A}})$ is a simple $($super$)$algebra if ${\mathcal{A}}$ is not an algebra of scalar multiplication. If ${\mathcal{A}}$ is a right-symmetric (super)algebra then $E({\mathcal{A}})$ is right-symmetric as well. Thus, we construct a wide class of simple (right-symmetric) (super)algebras which contains a matrix subalgebra with a common unity. We calculate the derivation algebra of the endomorph of a unital algebra ${\mathcal{A}}$ and the automorphism group of the simple right-symmetric algebra $E(V_{n})$$($the endomorph of a direct sum of fields$)$.