Local, 2-local derivations and biderivations on 3-parameter generalized quaternion

This article investigates the recently introduced three-parameter generalized quaternion algebra (3PGQ), denoted here as ${\mathbb{K}}_{{\lambda }_1,{\lambda }_2,{\lambda }_3}$ . Our analysis is structured in three parts. First, we demonstrate that every local and 2-local derivation on this algebra is automatically a derivation. Second, we provide a complete characterization of its biderivations. Finally, we describe its commuting maps and centroid.