Some properties of evolution algebras

Abstract

The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras the criterium of nilpotency is established in terms of the properties of corresponding matrices. Moreover, it is proved that for nilpotent n-dimensional complex evolution algebras the possible maximal nilpotency index is 1 + 2n-1. © 2013 The Korean Mathematical Society.