The algebraic and geometric classification of nilpotent terminal algebras
Abstract
We give algebraic and geometric classifications of -dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are one-parameter families of -dimensional nilpotent terminal (non-Leibniz) algebras, two-parameter families of -dimensional nilpotent terminal (non-Leibniz) algebras, three-parameter families of -dimensional nilpotent terminal (non-Leibniz) algebras, complemented by 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 -dimensional complex nilpotent terminal algebras.
Keywords
Cite
@article{arxiv.1909.00358,
title = {The algebraic and geometric classification of nilpotent terminal algebras},
author = {Ivan Kaygorodov and Mykola Khrypchenko and Yury Popov},
journal= {arXiv preprint arXiv:1909.00358},
year = {2021}
}