On evolution algebras

J. M. Casas; M. Ladra; B. A. Omirov; U. A. Rozikov

doi:10.1142/S1005386714000285

On evolution algebras

J. M. Casas
, M. Ladra
, B. A. Omirov
, U. A. Rozikov^*

^*Corresponding author for this work

University of Vigo
University of Santiago de Compostela
Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

Abstract

The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triangular matrices. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix, we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.

Original language	English
Pages (from-to)	331-342
Number of pages	12
Journal	Algebra Colloquium
Volume	21
Issue number	2
DOIs	https://doi.org/10.1142/S1005386714000285
State	Published - Jun 2014
Externally published	Yes

Keywords

Classification
Evolution algebra
Group of endomorphisms
Nil algebra
Right nilpotent algebra

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10.1142/S1005386714000285

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AB - The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triangular matrices. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix, we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.

KW - Classification

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KW - Group of endomorphisms

KW - Nil algebra

KW - Right nilpotent algebra

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On evolution algebras

Abstract

Keywords

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