Hyperquaternion Conformal Groups

The paper gives a new representation of conformal groups in n dimensions terms hyperquaternions defined as tensor products quaternion algebras (or subalgebra thereof). Being Clifford algebras, provide good pseudo-orthogonal such $$O(p+1,q+1)$$ isomorphic to the nD group with $$n=p+q.$$ yields simple expressions generators, independently matrices or operators. canonical decomposition and invariants are discussed. As application, 4D relativistic is detailed together worked example. Finally, formalism compared operator representation. Potential uses include particular, geometry, computer graphics field theory.