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Articles

A Geometric Interpretation of the Simplicity of SO(3)

Pages 340-350 | Received 14 Aug 2017, Accepted 10 Jan 2018, Published online: 22 Apr 2019

References

  • Artin, E. (1957). Geometric Algebra. New York: Interscience Publishers, Inc.
  • Berger, M. (2003). A Panoramic View of Riemannian Geometry. Berlin: Springer-Verlag.
  • Berger, M. (2009). Geometry I. (Translated from the 1977 French original by M. Cole and S. Levy, Fourth printing of the 1987 English translation.) Universitext. Berlin: Springer-Verlag.
  • Borel, A. (2001). Essays in the History of Lie Groups and Algebraic Groups, Vol. 21 of History of Mathematics. Providence, RI: American Mathematical Society/Cambridge: London Mathematical Society.
  • Bröcker, L. (1974). Zur orthogonalen Geometrie über pythagoreischen Körpern. J. Reine Angew. Math. 268/269: 68–77. (Collection of articles dedicated to Helmut Hasse on his seventy-fifth birthday, II.) doi.org/10.1515/crll.1974.268-269.68
  • Cartan, E. (1930). Sur les représentations linéaires des groupes clos. Comment. Math. Helv. 2(1): 269–283. DOI: 10.1007/BF01214464.
  • Cartan, E. (1932). Les espaces riemanniens symétriques. Verh. Internat. Math.-Kongr. Zürich. 1: 152–161.
  • Comfort, W. W., Robertson, L. C. (1987). Images and quotients of SO(3 , R): Remarks on a theorem of van der Waerden. Rocky Mountain J. Math. 17(1): 1–13. DOI: 10.1216/RMJ-1987-17-1-1.
  • Dieudonné, J. (1948). Sur les groupes classiques. Actualités Sci. Ind., no. 1040 = Publ. Inst. Math. Univ. Strasbourg (N.S.) 1 (1945). Paris: Hermann et Cie.
  • Grove, L. C. (2002). Classical Groups and Geometric Algebra. Graduate Studies in Mathematics, Vol. 39. Providence, RI: American Mathematical Society.
  • Hein, W. (1990). Einführung in die Struktur- und Darstellungstheorie der klassischen Gruppen. Hochschultext. [University Textbooks]. Berlin: Springer-Verlag. doi.org/10.1007/978-3-642-74340-5
  • Loos, O. (1969). Symmetric Spaces. I: General Theory. New York: W. A. Benjamin, Inc.
  • Neumaier, A., Westra, D. (2008). Classical and quantum mechanics via Lie algebras. arXiv preprint. arxiv.org/abs/0810.1019
  • Neumann, P. M., Stoy, G. A., Thompson, E. C. (1994). Groups and Geometry. Oxford Science Publications. New York: The Clarendon Press, Oxford Univ. Press. DOI: 10.1086/ahr/99.3.895-a.
  • Palais, B., Palais, R. (2007). Euler’s fixed point theorem: The axis of a rotation. J. Fixed Point Theory Appl. 2(2): 215–220. DOI: 10.1007/s11784-007-0042-5.
  • Palais, B., Palais, R., Rodi, S. (2009). A disorienting look at Euler’s theorem on the axis of a rotation. Amer. Math. Monthly. 116(10): 892–909. DOI: 10.4169/000298909X477014.
  • Perrin, D., Cabanes, M., Duchene, M. (1996). Cours d’algèbre, Vol. 30. Paris: Ellipses.
  • Rapinchuk, A. S. (2002). Algebraic and abstract simple groups: Old and new. Preprint.
  • Rees, E. G. (1988). Notes on Geometry, corrected, 2nd ed. Berlin: Springer-Verlag.
  • Stillwell, J. (2008). Naive Lie Theory. Undergraduate Texts in Mathematics. New York: Springer. doi.org/10.1007/978-0-387-78214-0
  • Stillwell, J. (2010). Mathematics and Its History, 3rd ed. Undergraduate Texts in Mathematics. New York: Springer. doi.org/10.1007/978-1-4419-6053-5
  • van der Waerden, B. L. (1933). Stetigkeitssätze für halbeinfache Liesche Gruppen. Math. Z. 36(1): 780–786. DOI: 10.1007/BF01188647.

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