On evolution operators in characteristic 2

Abstract

We are interested in the evolution operators defined on commutative and non-associative algebras when the characteristic of the scalar field is 2. We distinguish four types: nilpotent, quasi-constant, ultimately periodic, and plenary train operators. They are studied and classified for non-baric and for baric algebras.

Keywords:

• Baric algebras
• Bernstein algebras
• evolution algebras
• evolution operators
• periodic Bernstein algebras
• plenary train algebras
• quasi-constant algebras
• solvable algebras
• ultimately periodic operator

2010 MSC:

• Primary 17D92
• Secondary 17A30

Acknowledgements

I am grateful to anonymous referee whose the useful and detailed suggestions made it possible to clarify some points in this article.