A class of nilpotent evolution algebras. Issue 4 (3rd April 2019)

• Record Type: Journal Article
• Authors: Omirov, Bakhrom A.; Rozikov, Utkir A.; Velasco, M. Victoria
• Is Part Of: Communications in algebra. Volume 47:Issue 4(2019)
• Page Start: 1556
• Page End: 1567
• Publication Date: 2019-04-03
• Subjects: Evolution algebra -- nilpotent -- non-associative algebra; 17A60 -- 17D92; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1508584
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: 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.