On Dextral Symmetric Algebra

Abstract

We define the notion of dextral symmetric algebras (not necessarily associative), motivated by the idea of symmetric rings. We derive a complete classification of dextral symmetric algebras of Leavitt path algebras, and right Leibniz algebras up to dimension $4$. We also obtain that a finite-dimensional dextral symmetric right Leibniz algebra is solvable if and only if it satisfies a weaker notion of nilpotency.