The Jacobi Identity beyond Lie Algebras

Details The Jacobi Identity beyond Lie Algebras The Jacobi Identity beyond Lie Algebras

2009-04-07

arxiv.org/abs/0904.1155v3

Mathematics

Differential Geometry

Scientific paper

Frolicher and Nijenhuis recognized well in the middle of the previous century that the Lie bracket and its Jacobi identity could and should exist beyond Lie algebras. Nevertheless the conceptual meaning of their discovery has been obscured by the messy techniques they exploited. The principal objective in this paper is to show that the double dualization functor in a cartesian closed category as well as synthetic differential geometry provides an adequate framework, in which their discovery's conceptual meaning appears lucid.

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