A class of nilpotent evolution algebras
Rings and Algebras
2017-11-15 v1 Commutative Algebra
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 paper 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.
Cite
@article{arxiv.1711.05030,
title = {A class of nilpotent evolution algebras},
author = {B. A. Omirov and U. A. Rozikov and M. V. Velasco},
journal= {arXiv preprint arXiv:1711.05030},
year = {2017}
}
Comments
13 pages, 1 figure