The derivations of some evolution algebras

TL;DR

This paper studies the derivations of complex evolution algebras, showing that non-singular cases have no derivations and characterizing those with matrices of rank n-1.

Contribution

It provides a detailed analysis of derivation spaces for evolution algebras based on matrix rank, including new classifications for rank n-1 cases.

Findings

Derivations are zero for non-singular evolution algebras.

Derivation spaces are characterized for rank n-1 matrices.

Provides a classification based on matrix rank.

Abstract

In this work we investigate the derivations of $n-$dimensional complex evolution algebras, depending on the rank of the appropriate matrices. For evolution algebra with non-singular matrices we prove that the space of derivations is zero. The spaces of derivations for evolution algebras with matrices of rank $n-1$ are described.