The moduli space of 4-dimensional non-nilpotent complex associative algebras

摘要

In this paper we study the moduli space of 4-dimensional complex associativealgebras. We use extensions to compute the moduli space, and then give adecomposition of this moduli space into strata consisting of complex projectiveorbifolds, glued together through jump deformations. Because the space of4-dimensional algebras is large, we only classify the non-nilpotent algebras inthis paper.