On the non-linear cohomology of Lie equations. III

DOI10.4310/JDG/1214434608zbMath0452.58026OpenAlexW4249469724WikidataQ115189411 ScholiaQ115189411MaRDI QIDQ1148599

Hubert Goldschmidt, Donald Spencer

Publication date: 1978

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/jdg/1214434608

zbMATH Keywords

characteristic varietiesSpencer cohomologyclass of formally transitive Lie equations for which the integrability problem is not solvablecohomology of transitive Lie algebrasextensions of transitive Lie algebrasgeometric modules over transitive Lie algebraslifting of solutions of analytic Lie equationslinear cohomologylinear over- determined differential operator invariant under a transitive Lie equationnon-linear cohomologyobstruction to local solvabilityrealization as Lie equations on manifoldsrealization for geometric modules over real transitive Lie algebras

Mathematics Subject Classification ID

Infinite-dimensional Lie (super)algebras (17B65) Nonlinear higher-order PDEs (35G20) Jets in global analysis (58A20) Graded Lie (super)algebras (17B70) Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) (58H10) Partial differential equations on manifolds; differential operators (58J99) Cohomology of Lie (super)algebras (17B56) Pseudogroups and differentiable groupoids (58H05) Overdetermined problems for partial differential equations and systems of partial differential equations (35N99)

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The integrability problem for Lie equations

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