Non-degenerate evolution algebras

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URI: http://hdl.handle.net/10498/32352

DOI: 10.1016/J.JPAA.2023.107594

ISSN: 0022-4049

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Author/s
Calderón Martín, Antonio JesúsAuthority UCA; Fernández Ouaridi, AmirAuthority UCA; Kaygorodov, Ivan
Date
2024
Department
Matemáticas
Source
Journal of Pure and Applied Algebra - 2024, Vol. 228 n. 6 pp. 1-26
Abstract
In this paper we introduce a new invariant for a non-degenerate evolution algebra, which consists of an ordered sequence of evolution algebras of lower dimension, belonging all of them to a specific family. We use this invariant to propose a method to classify non-degenerate evolution algebras, and we apply it up to dimension 3. We also use it to describe the derivations of some families of evolution algebras and the degenerations of the variety of evolution algebras with square not greater than 1.
Subjects
Evolution algebra; Commutative algebra; Algebraic classification; Derivations; Irreducible component
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Attribution-NonCommercial 4.0 Internacional
This work is under a Creative Commons License Attribution-NonCommercial 4.0 Internacional