The Cohomology of Invariant Variational Bicomplexes

Ian M. Anderson and Juha Pohjanpelto
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Ian M. Anderson: Utah State University, Department of Mathematics
Juha Pohjanpelto: Oregon State University, Department of Mathematics

A chapter in Geometric and Algebraic Structures in Differential Equations, 1995, pp 3-19 from Springer

Abstract: Abstract Let π: E → M be a fiber bundle and let Γ be an infinitesimal Lie transformation group acting on E. We announce various new results concerning the cohomology of the Γ invariant variational bicomplex (Ω Γ *,* (J ∞(E)),d H ,d V ) and the associated Γ invariant Euler-Lagrange complex. As one application of our general theory, we completely solve the local invariant inverse problem of the calculus of variations for finite-dimensional infinitesimal Lie transformation groups.

Keywords: Vector Field; Regular Point; Source Form; Horizontal Connection; Continuous Cohomology (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0179-7_2

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DOI: 10.1007/978-94-009-0179-7_2

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