The Moduli Space of 3|2-dimensional Complex Associative Algebras

Abstract

We study the moduli space of 3|2-dimensional complex associative algebras. We use extensions to compute the moduli space, and then give a decomposition of this moduli space into strata consisting of complex projective orbifolds, glued together through jump deformations. This research project studies the non-nilpotent algebras, as they can be classified using the Fundamental Theorem on Non nilpotent finite dimensional algebras. The theory behind the construction of the algebras and the process of computing the deformations is explained in detail, as well as covering what algebras we have constructed and how they deform.