Z2-graded associative algebras arise both in physics and mathematics. We study here the 3|2-dimensional complex associative algebras, constructing the moduli space of isomorphism classes of such algebras using the notion of extensions of algebras of lower dimension. This is to say, we use our knowledge of lower dimensional algebras to construct the higher dimensional ones. Moreover, study the deformations of these algebras, which we analyze by computing a special type of deformation called a versal deformation. This moduli space is stratified by some projective orbifolds of a very simple type. We describe this stratification in this project. This talk will explain some of the research done with this project this past summer, at the NSF REU at UW-Eau Claire.
