[en] The stucture of the U(1) x SU(2) electroweak theory is constructable in a natural way on the Pauli algebra, P. P is isomorphic to the tensor product C x Q of the complexes and quaternions, two of the three division algebras, the octonions O the third. Following the pattern estabilished on P ≅ C x Q, an extended model is built upon C x Q x O. The gauge symmetry derived for this algebra is U(1) x SU(2) x SU(3), and in all other respects the model features that result exactly mirror the salient features of the standard model, including particle family replication