The algebraic and geometric classification of antiassociative algebras

Abstract

This paper is devoted to the complete algebraic and geometric classification of complex 4 and 5-dimensional antiassociative algebras. In particular, we proved that the variety of complex 4-dimensional antiassociative algebras has dimension 12 and it is defined by three irreducible components (in particular, there is only 1 rigid algebra in this variety); the variety of complex 5-dimensional antiassociative algebras has dimension 24 and it is defined by 8 irreducible components (in particular, there are only 4 rigid algebras in this variety).