The algebraic and geometric classification of nilpotent terminal algebras

Autor(es)

Kaygorodov, Ivan ^[1] ; Khrypchenko, Mykola ^{[2, 3]} ; Popov, Yury ^{[4, 5]}

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, CMCC, Av Estados 5001, BR-09210580 Santo Andre, SP - Brazil

^[2] Univ Fed Santa Catarina, Dept Matemat, Florianopolis, SC - Brazil

^[3] Univ Nova Lisboa, Fac Ciencias & Tecnol, Ctr Matemat & Aplicacoes, Caparica - Portugal

^[4] St Petersburg State Univ, St Petersburg - Russia

^[5] Univ Estadual Campinas, IMECC, Campinas - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Pure and Applied Algebra; v. 225, n. 6 JUN 2021.
• Citações Web of Science: 3

Resumo

We give algebraic and geometric classifications of 4-dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are 41 one-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 18 two-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 2 three-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, complemented by 21 additional isomorphism classes (see Theorem 13). The corresponding geometric variety has dimension 17 and decomposes into 3 irreducible components determined by the Zariski closures of a one-parameter family of algebras, a two-parameter family of algebras and a three-parameter family of algebras (see Theorem 15). In particular, there are no rigid 4-dimensional complex nilpotent terminal 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
• Processo FAPESP: 16/16445-0 - Representações das (super)álgebras do tipo de Jordan
• Beneficiário: Yury Popov
• Modalidade de apoio: Bolsas no Brasil - Doutorado