arXiv:1312.1721 [math.DG]AbstractReferencesReviewsResources
Cartan class of Invariant forms on Lie groups
Published 2013-12-05Version 1
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.
Comments: 29 pages
Journal: Differential Geometry and Applications 35 (2014), p 74 to p 94
Categories: math.DG
Keywords: lie group, cartan class, admit left invariant contact form, maximal compact subgroup, simple group sl
Tags: journal article
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