Classification in chains of three-dimensional real evolution algebras

Abstract

A chain of evolution algebras (CEA) is an uncountable family (depending on time) of evolution algebras on the field of real numbers. The matrix of structural constants of a CEA satisfies the Chapman-Kolmogorov equation. In this paper, we consider three CEAs of three-dimensional real evolution algebras. These CEAs depend on several (non-zero) functions defined on the set of time. For each chain we give a full classification (up to isomorphism) of the algebras depending on the time-parameter. We find concrete functions ensuring that the corresponding CEA contains all possible three-dimensional evolution algebras.

Keywords:

• Evolution algebra
• chain of evolution algebra
• Kolmogorov-Chapman equation
• isomorphism of algebras

2010 Mathematics Subject Classifications:

• 17D92
• 17D99

Acknowledgements

We thank both referees for helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).