Derivations and loops of some evolution algebras

TL;DR

This paper investigates the derivations of non-degenerate evolution algebras, introduces the concept of loops, and examines their invariance, advancing the understanding of algebraic structures related to evolution processes.

Contribution

It improves existing results on derivations of evolution algebras and introduces the notion of loops, analyzing their invariance under basis changes.

Findings

Enhanced description of derivations for n-dimensional Volterra evolution algebras

Introduction of the concept of loops in evolution algebras

Conditions for loop invariance under basis transformations

Abstract

In this work we study the space of derivations of non-degenerate evolution algebras. We improve some results obtained recently in the literature and, as a consequence, we advance in the description of the derivations for $n$-dimensional Volterra evolution algebras. In addition, we introduce the notion of loop of an evolution algebra and we analyze under which conditions the set of loops is invariant under change of basis.