| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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
Total Affiliations: 5
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| Document type: | Journal article |
| Source: | Journal of Pure and Applied Algebra; v. 225, n. 6 JUN 2021. |
| Web of Science Citations: | 3 |
| Abstract | |
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) | |
| FAPESP's process: | 18/09299-2 - Generalized derivations of non associative algebras |
| Grantee: | Ivan Kaygorodov |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - Brazil |
| FAPESP's process: | 18/15712-0 - Conservative algebras and superalgebras |
| Grantee: | Ivan Kaygorodov |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 16/16445-0 - Representations of (super)algebras of Jordan type |
| Grantee: | Yury Popov |
| Support Opportunities: | Scholarships in Brazil - Doctorate |