# The geometric classification of nilpotent algebras

#### Preprint

We give a geometric classification of $n$-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent algebras. We prove that the corresponding geometric varieties are irreducible, find their dimensions and describe explicit generic families of algebras which define each of these varieties. We show some applications of these results in the study of the length of anticommutative algebras.

Ivan Kaygorodov

Mykola Khrypchenko

### Publication

Year of publication: 2021