Georgian Mathematical Journal 09 (2002), No. 4, 723--774
Copyright Heldermann Verlag 2002
Differential Equations, Spencer Cohomology, and Computing Resolutions
Larry A. Lambe
Mathematics Division, School of Informatics, University of Wales, Bangor, Gwynedd LL57 1UT, Great Britain
Werner M. Seiler
Lehrstuhl f. Mathematik I, Universitaet Mannheim, 68131 Mannheim, Germany
We propose a new point of view of the Spencer cohomology appearing in the formal theory of differential equations based on a dual approach via comodules. It allows us to relate the Spencer cohomology with standard constructions in homological algebra and, in particular, to express it as a Cotor. We discuss concrete methods for its construction based on homological perturbation theory.
Keywords: Partial differential equation, Spencer cohomology, formal theory, homological resolution, comodules, cobar construction, symbolic computation.
MSC: 12Y05, 18G10, 18G15, 18G35, 18G60, 35G20, 35N99, 57T30, 68W30
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