LOCAL DERIVATIONS AND ROTA-BAXTER OPERATORS OF QUANTUM LOTKA-VOLTERRA ALGEBRAS ON M₂(C)

In this paper, we investigate in detail the local and 2-local derivations of the flow of quantum genetic Lotka-Volterra algebra belonging to M₂ (C). It aims to reveal how the different values of the parameter affect the different characteristic properties of these derivations. Our findings furnish structural details of the FQGLV-A algebras and develop the gap in actualizing local and 2-local derivations. We show that each local derivation is a derivation, and a set with 2-local derivations is a set of derivations. Further, we investigate the characterization of the Rota-Baxter operators in one of the considered scenar-ios with derivations to get better insights into the role and consequences of the algebraic structure of FQGLV-A.