Abstract
This paper is devoted to the complete algebraic and geometric classification of complex 4-dimensional nilpotent right commutative algebras. The corresponding geometric variety has dimension 15 and decomposes into 5 irreducible components determined by the Zariski closures of four one-parameter families of algebras and a two-parameter family of algebras (see Theorem B). In particular, there are no rigid complex 4-dimensional nilpotent right commutative algebras.
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