Derivations on four dimensional genetic Volterra algebra

TL;DR

This paper characterizes all derivations on four-dimensional genetic Volterra algebras and confirms that local derivations are indeed derivations, resolving a conjecture in the field.

Contribution

It provides a complete description of derivations on four-dimensional genetic Volterra algebras and proves that local derivations are derivations, confirming a prior conjecture.

Findings

All derivations on four-dimensional genetic Volterra algebras are described.

Any local derivation is a derivation of the algebra.

Confirmed the conjecture by Ganikhodzhaev et al.

Abstract

In this paper, we describe all derivations on four dimensional genetic Volterra algebras. We show that any local derivation is a derivation of the algebra. It is a positive answer to a conjecture made by Ganikhodzhaev, Mukhamedov, Pirnapasov and Qaralleh.