The evolution operator of evolution algebras

Abstract

This paper deals with the evolution operator of evolution algebras. The main goal is to obtain novel results of this operator, both in the case in which it is a derivation and when it is a homomorphism of algebras. These new results constitute a criterion for classifying evolution algebras satisfying one of these conditions. An algorithm to obtain all these degenerate evolution algebras starting from those of smaller dimensions is also constructed.

Keywords:

• Evolution operator
• evolution algebras
• algorithm

2010 Mathematics Subject Classifications:

• 47C05
• 17D92
• 17A36
• 17A20

Disclosure statement

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

Additional information

Funding

This work was supported by Consejería de Economía, Innovación, Ciencia y Empleo, Junta de Andalucía Research Group FQM-326.