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arXiv · 1909.00358

The algebraic and geometric classification of nilpotent terminal algebras

Ivan Kaygorodov·Mykola Khrypchenko·Yury Popov
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Abstract

We give algebraic and geometric classifications of $4$-dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are $41$ one-parameter families of $4$-dimensional nilpotent terminal (non-Leibniz) algebras, $18$ two-parameter families of $4$-dimensional nilpotent terminal (non-Leibniz) algebras, $2$ three-parameter families of $4$-dimensional nilpotent terminal (non-Leibniz) algebras, complemented by $21$ additional isomorphism classes. The corresponding geometric variety has dimension 17 and decomposes into 3 irreducible components determined by the Zariski closures of a one-parameter family of algebras, a two-parameter family of algebras and a three-parameter family of algebras. In particular, there are no rigid $4$-dimensional complex nilpotent terminal algebras.

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Ivan Kaygorodov, Mykola Khrypchenko, Yury Popov. 2019-09-01. The algebraic and geometric classification of nilpotent terminal algebras. https://doi.org/10.1016/j.jpaa.2020.106625

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