Skew-supersymmetric solution of the super Malcev Yang-Baxter equation and Pre-Malcev superalgebras

TL;DR

This paper introduces pre-Malcev superalgebras as a new algebraic framework linked to super $ ext{O}$-operators and explores their relationship with the super Malcev Yang-Baxter equation, enriching the understanding of algebraic structures in superalgebra theory.

Contribution

It defines pre-Malcev superalgebras, establishes their relations with Malcev superalgebras and pre-alternative superalgebras, and connects these to the super Yang-Baxter equation via super $ ext{O}$-operators.

Findings

Introduction of pre-Malcev superalgebras as algebraic structures behind super $ ext{O}$-operators.

Established relations among Malcev, pre-Malcev, and pre-alternative superalgebras.

Explored the operator forms of the classical Yang-Baxter equation in Malcev superalgebras.

Abstract

The purpose of this paper is to introduce the notion of pre-Malcev superalgebras as the algebraic structure behind the super $\mathcal{O}$-operators on Malcev superalgebras. Moreover, the relations among Malcev superalgebras, pre-Malcev superalgebras and pre-alternative superalgebras are established. Then, we study the operator forms of the classical Yang-Baxter equation (CYBE) in Malcev superalgebras and give their relationship with super $\mathcal{O}$-operators. There are close relationships between the CYBE in Malcev superalgebras and pre-Malcev superalgebras which can be interpreted through the super $\mathcal{O}$-operators.