On evolution algebras. (English) Zbl 1367.17026
Summary: 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.
MSC:
17D92 | Genetic algebras |
Keywords:
evolution algebra; nil algebra; right nilpotent algebra; group of endomorphisms; classificationSoftware:
MathematicaReferences:
[1] | DOI: 10.4134/BKMS.2013.50.5.1481 · Zbl 1278.05120 · doi:10.4134/BKMS.2013.50.5.1481 |
[2] | DOI: 10.1007/BF01297739 · Zbl 0446.16033 · doi:10.1007/BF01297739 |
[3] | DOI: 10.1134/S1995080211040202 · Zbl 1260.46031 · doi:10.1134/S1995080211040202 |
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