On $\exp(Der(E))$ of nilpotent evolution algebras

Abstract

In the present paper, every evolution algebra is endowed with Banach algebra norm. This together with the description of derivations and automorphisms of nilpotent evolution algebras, allows to investigated the set exp(Der(E)). Moreover, it is proved that exp(Der(E)) is a normal subgroup of Aut(E), and its corresponding index is calculated.