• Corpus ID: 50818244

G2 and the Rolling Ball

  title={G2 and the Rolling Ball},
  author={John C. Baez and John Huerta},
  journal={arXiv: Differential Geometry},
Understanding the exceptional Lie groups as the symmetry groups of simpler objects is a long-standing program in mathematics. Here, we explore one famous realization of the smallest exceptional Lie group, G2. Its Lie algebra acts locally as the symmetries of a ball rolling on a larger ball, but only when the ratio of radii is 1:3. Using the split octonions, we devise a similar, but more global, picture of G2: it acts as the symmetries of a 'spinorial ball rolling on a projective plane', again… 
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