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Differential Systems Associated with Tableaux over Lie Algebras

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Symmetries and Overdetermined Systems of Partial Differential Equations

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 144))

Abstract

We give an account of the construction of exterior differential systems based on the notion of tableaux over Lie algebras as developed in [33]. 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.

Partially supported by MIUR project Metriche riemanniane e varietà differenziali, and by the GNSAGA of INDAM.

Partially supported by MIUR project Proprietà geometriche delle varietà reali e complesse, and by the GNSAGA of INDAM.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica Pura ed Applicata, Università degli Studi dell’Aquila, Via Vetoio, 1-67010, Coppito (L’Aquila), Italy

    Emilio Musso

  2. Dipartimento di Matematica, Università degli Studi di Parma, Viale G.P. Usberti 53/A - Campus universitario, 1-43100, Parma, Italy

    Lorenzo Nicolodi

Authors
  1. Emilio Musso
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  2. Lorenzo Nicolodi
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, The University of Adelaide, SA, 5005, Australia

    Michael Eastwood

  2. School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. SE, Minneapolis, MN, 55455

    Willard Miller Jr.

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Musso, E., Nicolodi, L. (2008). Differential Systems Associated with Tableaux over Lie Algebras. In: Eastwood, M., Miller, W. (eds) Symmetries and Overdetermined Systems of Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 144. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73831-4_26

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