On the lie group structure of quaternions

In this thesis firstly, dual numbers, real quaternions dual quaternions, split quaternions and dual split quaternions and their properties are examined in detail. Afterwards, Lie group structures and Lie algebra structures on the sets of unit real quaternions, unit dual quaternions, unit split quaternions and unit split dual quaternions are considered and their matrix representations are found. Also, adjoint representations and Killing bilinear forms of these groups are found and it is shown that their adjoint representations correspond to a rotation.