The algebraic and geometric classification of nilpotent terminal algebras

Ivan Kaygorodov, Mykola Khrypchenko, Yury Popov

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

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 (see Theorem 13). 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 (see Theorem 15). In particular, there are no rigid 4-dimensional complex nilpotent terminal algebras.

Original languageEnglish
Article number106625
JournalJournal Of Pure And Applied Algebra
Volume225
Issue number6
DOIs
Publication statusPublished - Jun 2021

Keywords

  • Algebraic classification
  • Geometric classification
  • Leibniz algebra
  • Nilpotent algebra
  • Terminal algebra

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