On nilpotent index and dibaricity of evolution algebras

2012/08/08 by J. M. Casas, M. Ladra, Casas, J. M. +5
Computer Science · Mathematics · #17D92 #17D99 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1208.1709

openalex publication_date 2012/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An evolution algebra corresponds to a quadratic matrix A of structural constants. It is known the equivalence between nil, right nilpotent evolution algebras and evolution algebras which are defined by upper triangular matrices A. We establish a criterion for an n-dimensional nilpotent evolution algebra to be with maximal nilpotent index 2^n-1+1. We give the classification of finite-dimensional complex evolution algebras with maximal nilpotent index. Moreover, for any s=1,...,n-1 we construct a wide class of n-dimensional evolution algebras with nilpotent index 2^n-s+1. We show that nilpotent evolution algebras are not dibaric and establish a criterion for two-dimensional real evolution algebras to be dibaric.

Related

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• Approximation of an algebra by evolution algebras
• A class of nilpotent evolution algebras
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• On the property of subalgebras of Evolution algebras