Chains in evolution algebras

In this work we approach three-dimensional evolution algebras from certain constructions performed on two-dimensional algebras. More precisely, we provide four different constructions producing three-dimensional evolution algebras from two-dimensional algebras. Also we introduce two parameters, the...

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Bibliographic Details
Published in:Linear algebra and its applications 2021-08, Vol.622, p.104-149
Main Authors: Cabrera Casado, Yolanda, Cardoso Gonçalves, Maria Inez, Gonçalves, Daniel, Martín Barquero, Dolores, Martín González, Cándido
Format: Article
Language:English
Subjects:
Algebra
Annihilator
Diagonalizable evolution algebra
Evolution
Evolution algebra
Isomorphism
Linear algebra
Socle
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Summary:In this work we approach three-dimensional evolution algebras from certain constructions performed on two-dimensional algebras. More precisely, we provide four different constructions producing three-dimensional evolution algebras from two-dimensional algebras. Also we introduce two parameters, the annihilator stabilizing index and the socle stabilizing index, which are useful tools in the classification theory of these algebras. Finally, we use moduli sets as a convenient way to describe isomorphism classes of algebras.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.03.026