The algebraic and geometric classification of nilpotent anticommutative algebras

Autor(es)

Kaygorodov, Ivan ^{[1, 2]} ; Khrypchenko, Mykola ^{[3, 4]} ; Lopes, Samuel A. ^[5]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, CMCC, Santo Andre, SP - Brazil

^[2] Siberian Fed Univ, Krasnoyarsk - Russia

^[3] Univ Fed Santa Catarina, Dept Matemat, Florianopolis, SC - Brazil

^[4] Univ Nova Lisboa, Fac Ciencias & Tecnol, Ctr Matemat & Aplicacoes, Caparica - Portugal

^[5] Univ Porto, Fac Ciencias, CMUP, Rua Campo Alegre 687, P-4169007 Porto - Portugal

• Tipo de documento: Artigo Científico
• Fonte: Journal of Pure and Applied Algebra; v. 224, n. 8 AUG 2020.
• Citações Web of Science: 10

Resumo

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. (C) 2020 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 18/09299-2 - Derivações gerais de álgebras não associativas
• Beneficiário: Ivan Kaygorodov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil
• Processo FAPESP: 18/15712-0 - Álgebras e superálgebras conservativas
• Beneficiário: Ivan Kaygorodov
• Modalidade de apoio: Auxílio à Pesquisa - Regular