The algebraic and geometric classification of nilpotent anticommutative algebras

Ivan Kaygorodov, Mykola Khrypchenko, Samuel A. Lopes

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

We give algebraic and geometric classifications of 6-dimensional complex nilpotent anticommutative algebras. Specifically, we find that, up to isomorphism, there are 14 one-parameter families of 6-dimensional nilpotent anticommutative algebras, complemented by 130 additional isomorphism classes. The corresponding geometric variety is irreducible and determined by the Zariski closure of a one-parameter family of algebras. In particular, there are no rigid 6-dimensional complex nilpotent anticommutative algebras.

Original languageEnglish
Article number106337
JournalJournal Of Pure And Applied Algebra
Volume224
Issue number8
DOIs
Publication statusPublished - Aug 2020

Keywords

  • Algebraic classification
  • Anticommutative algebra
  • Geometric classification
  • Nilpotent algebra

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