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Modular orthogonal groups in four dimensions

Published online by Cambridge University Press:  24 October 2008

Ifor Morris
Ifor Morris
Affiliation:
University College of North Wales, Bangor
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Extract

Littlewood has shown(1) that any rotation in 4 dimensions can be expressed as the resultant of a right-handed and a left-handed rotation, and that every right-handed rotation commutes with every left-handed rotation. It follows that the rotation group in 4 dimensions is expressible in some way as the product of two groups of right-handed and left-handed rotations, respectively.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 2 , April 1961 , pp. 239 - 246
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Littlewood, D. E., The groups of the regular solids in n-dimensions. Proc. London Math. Soc. (2), 32 (1929), 10–20.Google Scholar
(2)Dickson, L. E., Linear groups (Leipzig, 1901).Google Scholar