Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-22T05:18:39.299Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

1. Artin, E., Geometric Algebra, Interscience Tracts No. 3, New York-London, Interscience Publications, 1957.Google Scholar
2. Baer, R., Linear Algebra and Projective Geometry, New York, Academic Press, 1952.Google Scholar
3. Dieudonné, J., Sur les générateurs des groupes classiques, Summa Bras. Math. 3 (1955), pp. 149-178.Google Scholar
4. Dieudonné, J., La géométrie des groupes classiques, (Trois. Ed.) Ergeb. d. Math. 5; Springer Verlag, 1971.Google Scholar
5. Ellers, E. W., Length of a unitary transformation of characteristic 2, J. reine angew. Math. 281 (1976) pp. 6-12.Google Scholar
6. Ellers, E. W., The length of a unitary transformation, J. reine angew. 281 (1976) pp. 1-5.Google Scholar
7. Ellers, E. W. and Patton, R., Zur geschichte der Erzeugnis von Bewegungsgruppen, Mitteil. Math. Ges. Hamburg, X, 2, 1973.Google Scholar
8. Huppert, B., Geometric Algebra, Lecture Notes, University of Illinois at Chicago Circle, 1970.Google Scholar
9. Meyer, K-H., Transvektionsrelationen in metrischen Vektorräumen der Charakteristik 2, J. reine angew. Math. 233 (1968), 189-199.Google Scholar
10. Scherk, P., On the decomposition of orthogonalities into symmetries, Proc. Amer. Soc. 1 (1950), 481-491.Google Scholar