Differential systems associated with tableaux over Lie algebras

Details Differential systems associated with tableaux over Lie algebras Differential systems associated with tableaux over Lie algebras

2007-05-18

arxiv.org/abs/0705.2715v1

IMA Vol. Math. Appl., 144, Springer, New York, 2008, 497-514

Mathematics

Differential Geometry

16 pages; to appear in: "Symmetries and Overdetermined Systems of Partial Differential Equations" (M. Eastwood and W. Miller,

Scientific paper

We give an account of the construction of exterior differential systems based on the notion of tableaux over Lie algebras as developed in [Comm. Anal. Geom 14 (2006), 475-496; math.DG/0412169]. The definition of a tableau over a Lie algebra is revisited and extended in the light of the formalism of the Spencer cohomology; the question of involutiveness for the associated systems and their prolongations is addressed; examples are discussed.

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