Split octonions and generic rank two distributions in dimension five
Katja Sagerschnig (2006)
Archivum Mathematicum
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In his famous five variables paper Elie Cartan showed that one can canonically associate to a generic rank 2 distribution on a 5 dimensional manifold a Cartan geometry modeled on the homogeneous space , where is one of the maximal parabolic subgroups of the exceptional Lie group . In this article, we use the algebra of split octonions to give an explicit global description of the distribution corresponding to the homogeneous model.