The geometric classification of nilpotent algebras

Abstract

We give a geometric classification of n-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent al-gebras. 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. & COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).