# Evolution algebras, automorphisms, and graphs

## TL;DR

This paper explores the automorphism groups and derivations of evolution algebras, revealing their dependence on associated graphs and providing explicit descriptions, especially in characteristic 0 or 2.

## Contribution

It establishes an exact sequence for automorphism groups of evolution algebras and characterizes their derivations based on the underlying graph structure.

## Key findings

- Automorphism group scheme fits into an exact sequence determined by the graph.
- Derivations are trivial in characteristic 0 or 2, and abelian otherwise.
- Explicit descriptions of derivations depend solely on the associated graph.

## Abstract

The affine group scheme of automorphisms of an evolution algebra that is equal to its square, is shown to lie in an exact sequence, such that the other terms depend solely on the directed graph associated to the algebra. As a consequence, the Lie algebra of derivations is shown to be trivial in characteristic 0 or 2, and to be abelian, with a precise description depending just on the graph, otherwise.