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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].

##### MSC:
 17B66 Lie algebras of vector fields and related (super) algebras 58A30 Vector distributions (subbundles of the tangent bundles)
##### Keywords:
Lie algebra of infinitesimal automorphisms; jet space