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Differential systems associated with simple graded Lie algebras. (English) Zbl 0812.17018
Shiohama, K. (ed.), Progress in differential geometry. Tokyo: Kinokuniya Company Ltd.. Adv. Stud. Pure Math. 22, 413-494 (1993).
This paper is based on the lectures given at University of Minnesota in 1990-91. Let \({\mathfrak g}= \oplus_{p\in Z} {\mathfrak g}_ p\) be a real simple Lie algebra such that \([{\mathfrak g}_ p, {\mathfrak g}_ q] \subset {\mathfrak g}_{p+q}\) and \(G'\) be the normalizer of \(\oplus_{p\geq 0} {\mathfrak g}_ p\) in the adjoint group \(G\). Then there is a \(G\)-invariant differential system \(D_{\mathfrak g}\) on \(M= G/G'\). The main result is the following. The Lie algebra of all infinitesimal automorphisms of \((M,D_{\mathfrak g})\) is isomorphic to \({\mathfrak g}\) except when it is locally isomorphic to the contact system on a real or complex jet space.
For the entire collection see [Zbl 0779.00011].

17B66 Lie algebras of vector fields and related (super) algebras
58A30 Vector distributions (subbundles of the tangent bundles)