English

The algebraic and geometric classification of nilpotent terminal algebras

Rings and Algebras 2021-11-02 v2

Abstract

We give algebraic and geometric classifications of 44-dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are 4141 one-parameter families of 44-dimensional nilpotent terminal (non-Leibniz) algebras, 1818 two-parameter families of 44-dimensional nilpotent terminal (non-Leibniz) algebras, 22 three-parameter families of 44-dimensional nilpotent terminal (non-Leibniz) algebras, complemented by 2121 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 44-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}
}