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SO(3) and Sp(1)

  • Morton L. Curtis
Chapter
Part of the Universitext book series (UTX)

Abstract

We have seen that Sp(l) , which is all quaternions of unit length, is just the unit 3-sphere in ℝ4 ( = ℍ) . Also we have seen that dim \(SO\left( 3 \right) = \frac{{3 \cdot 2}}{2} = 3\) . So dimension won’t distinguish S3 from SO(3) , and, for all we know now, they might be isomorphic. In this section we define and study an “almost isomorphism” between them.

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Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  • Morton L. Curtis
    • 1
  1. 1.Department of MathematicsRice University, Weiss School of Natural SciencesHoustonUSA

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