Derivations of generalized quaternion algebra

Abstract

The purpose of this paper is to determine derivations of the algebra H-alpha,H-beta of generalized quaternions over the reals and hence to obtain the algebra Der(H-alpha,H-beta) of derivations of H-alpha,H-beta. Once we know derivations we might decompose Der(H-alpha,H-beta) in terms of its inner and/or central derivations whenever they exist. Apart from Der(H-alpha,H-beta) we would also be able to obtain generalized derivations, which have been studied by analysts in the context of algebras of some normed spaces, and of prime and semiprime rings.