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Singular Isometries in Orthogonal Groups

Published online by Cambridge University Press:  20 November 2018

Georg Gunther
Georg Gunther*
Affiliation:
Scarborough College, University of Toronto, TorontoOntarioCanada
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In this paper, we study the behaviour of singular isometries in orthogonal groups. These are isometries whose path is a singular subspace. We shall prove that the path of such a singular isometry is always even-dimensional. We shall use this result to show that the subgroup of the orthogonal group On(K, Q) which is generated by the singular isometries is the commutator subgroup Ωn(K, Q).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 2 , 01 June 1977 , pp. 189 - 198
Copyright
Copyright © Canadian Mathematical Society 1977

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