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SO(3) and Sp(1)

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

Abstract

We have seen that Sp(1), which is all quaternions of unit length, is just the unit 3-sphere in R4 ( = ℍ). Also we have seen that dim \( {\text{SO(3) = }}\frac{{3\; \cdot \;2}}{2}\; = \;3\;. \) 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. 1979

Authors and Affiliations

  • Morton L. Curtis
    • 1
  1. 1.Department of MathematicsRice UniversityHoustonUSA

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