Local derivations and Rota-Baxter operators of quantum Lotka-Volterra algebras on M_2(C)

In this paper, we thoroughly investigate the local and 2-local derivations of a flow of quantumgenetic Lotka-Volterra algebras on M2(C) (FQGLV-A). The analysis is mainly geared towards understanding how specific parameter values influence the properties of these derivations. Our findings elucidate the structural intricacies of FQGLV-A algebras and bridge gaps in the current understanding of local and 2-local derivations. We prove that any local derivation is indeed a derivation. Furthermore, the set of2-local deviations coincide with the set of deviations.