On evolution algebras

Abstract

The structural constants of an evolution algebra is given by a quadratic matrix $A$. In this work we establish equivalence between nil, right nilpotent evolution algebras and evolution algebras, which are defined by upper triangular matrix $A$. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix $A$ we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.

17 pages