A class of nilpotent evolution algebras

Recently, by A. Elduque and A. Labra a new technique and a type of an evolution algebra are introduced. Several nilpotent evolution algebras defined in terms of bilinear forms and symmetric endomorphisms are constructed. The technique then used for the classification of the nilpotent evolution algeb...

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Bibliographic Details
Published in:Communications in algebra 2019-04, Vol.47 (4), p.1556-1567
Main Authors: Omirov, Bakhrom A., Rozikov, Utkir A., Velasco, M. Victoria
Format: Article
Language:English
Subjects:
Algebra
Evolution
Evolution algebra
nilpotent
non-associative algebra
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Summary:Recently, by A. Elduque and A. Labra a new technique and a type of an evolution algebra are introduced. Several nilpotent evolution algebras defined in terms of bilinear forms and symmetric endomorphisms are constructed. The technique then used for the classification of the nilpotent evolution algebras up to dimension five. In this article, we develop this technique for high dimensional evolution algebras. We construct nilpotent evolution algebras of any type. Moreover, we show that, except the cases considered by Elduque and Labra, this construction of nilpotent evolution algebras does not give all possible nilpotent evolution algebras.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2018.1508584