On nilpotent index and dibaricity of evolution algebras

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 alg...

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Bibliographic Details
Published in:Linear algebra and its applications 2013-07, Vol.439 (1), p.90-105
Main Authors: Casas, J.M., Ladra, M., Omirov, B.A., Rozikov, U.A.
Format: Article
Language:English
Subjects:
Classification
Dibaric algebra
Evolution algebra
Nilpotent algebra
Nilpotent index
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Summary: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 2n-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 2n-s+1. We show that nilpotent evolution algebras are not dibaric and establish a criterion for two-dimensional real evolution algebras to be dibaric.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2013.03.006