Derivations of generalized quaternion algebra

Abstract

The purpose of this paper is to determine derivations of the algebra Hα,β of generalized quaternions over thereals and hence to obtain the algebra Der(Hα,β) of derivations of Hα,β . Once we know derivations we might decomposeDer(Hα,β) in terms of its inner and/or central derivations whenever they exist. Apart from Der(Hα,β) we would alsobe able to obtain generalized derivations, which have been studied by analysts in the context of algebras of some normedspaces, and of prime and semiprime rings.