As the biquaternions have been a fixture of linear algebra since the beginnings of mathematical physics, there is an array of concepts that are illustrated or represented by biquaternion algebra. The transformation group formula_28 has two parts, formula_29 and formula_30 The first part is characterized by formula_31 ; then the Lorentz transformation corresponding to is given by formula_32 since formula_33 Such a transformation is a rotation by quaternion multiplication, and the collection of them is O(3) formula_34 But this subgroup of is not a normal subgroup, so no quotient group can be formed.