Degenerations of nilpotent algebras

Amir Fernández Ouaridi, Ivan Kaygorodov, Mykola Khrypchenko, Yury Volkov

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


We give a complete description of the primary degenerations and non-degenerations between the 3-dimensional nilpotent algebras, the 4-dimensional nilpotent commutative algebras and the 5-dimensional nilpotent anticommutative algebras over C. It follows that all the varieties under consideration are irreducible and determined by the rigid algebra N2, the family of algebras C19(α) and the rigid algebra A11, respectively. In particular, as an auxiliary new result, we obtain an algebraic classification of the 4-dimensional complex nilpotent commutative algebras.

Original languageEnglish
Article number106850
Pages (from-to)1-21
Number of pages21
JournalJournal Of Pure And Applied Algebra
Issue number3
Publication statusPublished - Mar 2022


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


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