Deformations of 5 Dimensional Complex Non-nilpotent Associative Algebras

Algebraic structures are common objects of study for undergraduates in physics and mathematics. In our research, we look at the deformations of algebras in a given moduli space. Deformations of an algebra are made by introducing a new parameter to the existing set of rules and examining what the resulting algebra is isomorphic to. The moduli space in our research comprises all complex 5-dimensional non nilpotent associative algebras. According to our findings, there are 285 isomorphism classes of algebras, including 16 one-parameter families. Each of these families is parametrized by a 1-dimensional projective orbifold. With the help of the computer algebra system Maple, we have computed versal deformations for nearly all of these algebras, and have completed the study of these deformations for almost all of the algebras. By computing the miniversal deformation of an algebra, we can determine precisely which algebras it deforms to. With this information, we will be able to understand how the moduli space of such algebras is naturally glued together