Symmetrization of Brace Algebras

TL;DR

This paper demonstrates that applying symmetrization to a brace algebra results in a symmetric brace algebra, establishing a fundamental connection between these algebraic structures.

Contribution

It introduces a method to derive symmetric brace algebras from brace algebras through symmetrization, revealing a new structural relationship.

Findings

Symmetrization transforms brace algebras into symmetric brace algebras.

The process preserves algebraic properties relevant to symmetry.

Provides a foundation for further exploration of symmetric structures.

Abstract

We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra.