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