On Dextral Symmetric Algebra

TL;DR

This paper introduces dextral symmetric algebras, classifies them in specific algebraic contexts, and explores their properties, including solvability criteria for finite-dimensional cases.

Contribution

It defines dextral symmetric algebras and provides a complete classification for certain algebra types, advancing understanding of their structure and properties.

Findings

Complete classification of dextral symmetric Leavitt path algebras

Classification of right Leibniz algebras up to dimension 4

Finite-dimensional dextral symmetric right Leibniz algebras are solvable if and only if weakly nilpotent

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.