| 21. | Such a hypersurface, called a quasi-sphere, is preserved by the appropriate indefinite orthogonal group.
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| 22. | The subgroup of orthogonal matrices with determinant is called the " special orthogonal group ", denoted.
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| 23. | Over, one replaces by the orthogonal group, and by restricting to orthonormal frames, one gets the identity
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| 24. | Similarly there is a homomorphism from the Spin group to the special orthogonal group of " V ".
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| 25. | It covered symmetric groups, general linear groups, orthogonal groups, and symplectic groups and results on their representations.
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| 26. | In even dimension, the middle group is known as the split orthogonal group, and is of particular interest.
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| 27. | The special orthogonal group SO ( " N " ) has irreducible ordinary and spin representations labelled by signatures
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| 28. | In the case of the symmetries of a sphere, the matrix group is the orthogonal group of three dimensions.
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| 29. | Moreover, the diffeomorphism group of the circle has the homotopy-type of the orthogonal group O ( 2 ).
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| 30. | There is also the connecting homomorphism from of the orthogonal group, to the of the kernel of the spin covering.
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