11. The structure group is the orthogonal group . 12. The circle group is therefore isomorphic to the special orthogonal group SO ( 2 ). 13. In particular, the space of spinors is a projective representation of the orthogonal group . 14. The orthogonal group , consisting of all proper and improper rotations, is generated by reflections. 15. If the gauge symmetry is an orthogonal group then this class is the first Pontrjagin class. 16. This structure theory is compatible with the action of the pseudo-orthogonal groups plus dilatations. 17. The Cartan Dieudonn?theorem describes the structure of the orthogonal group for a non-singular form. 18. Thus reflections generate the orthogonal group , and this result is known as the Cartan Dieudonn?theorem. 19. The Lie algebra of the generalized orthogonal group o ( 1, n ) is given by matrices 20. Recall from the previous section that there is a homomorphism from the Clifford group onto the orthogonal group .
