The algebraic and geometric classification of right alternative superalgebras

TL;DR

This paper classifies complex 3-dimensional right alternative superalgebras algebraically and geometrically, also providing classifications for related algebraic structures such as associative and permutative superalgebras.

Contribution

It offers the first comprehensive algebraic and geometric classification of 3-dimensional right alternative superalgebras and related algebraic varieties.

Findings

Complete algebraic classification of 3D right alternative superalgebras

Geometric classification of the algebraic variety of these superalgebras

Classification results for related algebraic structures like associative and permutative superalgebras

Abstract

The algebraic and geometric classifications of complex $3$-dimensional right alternative superalgebras are given. As a byproduct, we have the algebraic and geometric classification of the variety of $3$-dimensional $\mathfrak{perm}$, binary $\mathfrak{perm}$, associative, binary associative, $\big(-1,1\big)$-, and binary $\big(-1,1\big)$-superalgebras.