# The algebraic and geometric classification of nilpotent left-symmetric algebras

@inproceedings{Adashev2021TheAA,
title={The algebraic and geometric classification of nilpotent left-symmetric algebras},
author={Jobir Q. Adashev and Ivan Kaygorodov and A. Kh. Khudoyberdiyev and Aloberdi Sattarov},
year={2021}
}
This paper is devoted to the complete algebraic and geometric classification of complex 4dimensional nilpotent left-symmetric algebras. The corresponding geometric variety has dimension 15 and decomposes into 3 irreducible components determined by the Zariski closures of two oneparameter families of algebras and a two-parameter family of algebras (see Theorem B). In particular, there are no rigid 4-dimensional complex nilpotent left symmetric algebras.

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