The algebraic and geometric classification of nilpotent right commutative algebras (Q2034870)

In this paper, the authors give a complete algebraic and geometric classification of complex 4-dimensional nilpotent right commutative algebras. In Theorem A, they prove that a complex 4-dimensional nilpotent right commutative algebra is a Novikov algebra or it is isomorphic to an algebra A, with the classification given in a table which includes all cases. They prove that the corresponding geometric variety has dimension 15 and has a decomposition in 5 irreducible components determined by the Zariski closures of four one-parameter families of algebras and a two-parameter family of algebras. The result has been done in Theorem B, followed by a table in which all cases are presented.