The algebraic and geometric classification of right alternative 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.