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arXiv · 1312.1721

Cartan class of Invariant forms on Lie groups

Michel Goze·Elisabeth Remm
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Abstract

We are interested in the class, in the Elie Cartan sense, of left invariant forms on a Lie group. We construct the class of Lie algebras provided with a contact form and classify the frobeniusian Lie algebras up to a contraction. We also study forms which are invariant by a subgroup. We show that the simple group SL(2n,R) which doesn't admit left invariant contact form, yet admits a contact form which is invariant by a maximal compact subgroup. We determine also Pfaffian forms on the Heisenberg $3$-dimensional group invariant by a subgroup and obtain the Transport Equation.

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Michel Goze, Elisabeth Remm. 2013-12-05. Cartan class of Invariant forms on Lie groups. https://doi.org/10.1016/j.difgeo.2014.05.008

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