Displaying similar documents to “Generic one-step bracket-generating distributions of rank four”

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 G ˜ 2 / P , where P is one of the maximal parabolic subgroups of the exceptional Lie group G ˜ 2 . In this article, we use the algebra of split octonions to give an explicit global description of the distribution corresponding to the homogeneous model.

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.