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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Degenerations of nilpotent algebras

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Author(s):
Ouaridi, Amir Fernandez [1] ; Kaygorodov, Ivan [2, 3, 4] ; Khrypchenko, Mykola [5, 6] ; Volkov, Yury [7]
Total Authors: 4
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
Total Affiliations: 7
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