Degenerations of nilpotent algebras

Author(s)

Ouaridi, Amir Fernandez ^[1] ; Kaygorodov, Ivan ^{[2, 3, 4]} ; Khrypchenko, Mykola ^{[5, 6]} ; Volkov, Yury ^[7]

Affiliation

^[1] Univ Cadiz, Cadiz - Spain

^[2] Univ Fed ABC, CMCC, Santo Andre, SP - Brazil

^[3] Univ Porto, CMUP, Fac Ciencias, Porto - Portugal

^[4] Moscow Ctr Fundamental & Appl Math, Moscow - Russia

^[5] Univ Fed Santa Catarina, Dept Matemat, Florianopolis, SC - Brazil

^[6] Univ Nova Lisboa, Dept Matemat, Fac Ciencias & Tecnol, Caparica - Portugal

^[7] St Petersburg Univ, St Petersburg - Russia

• Document type: Journal article
• Source: Journal of Pure and Applied Algebra; v. 226, n. 3 MAR 2022.
• Web of Science Citations: 0

Abstract

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 N-2, the family of algebras C-19(alpha) and the rigid algebra A(11), respectively. In particular, as an auxiliary new result, we obtain an algebraic classification of the 4-dimensional complex nilpotent commutative algebras. (C) 2021 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 18/15712-0 - Conservative algebras and superalgebras
• Grantee: Ivan Kaygorodov
• Support Opportunities: Regular Research Grants