Titlebook: Geometric and Algebraic Structures in Differential Equations; P. H. M. Kersten,I. S. Krasil’Shchik Book 1995 Kluwer Academic Publishers 19

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Spencer Cohomologies and Symmetry Groups,manage to unify computations by reduction to the invariant systems over a homogeneous space. The conditions of coincidence of Spencer cohomologies with the cohomologies of an invariant Spencer complex we obtain from the arithmetic of a ℂ-characteristic manifold with respect to fundamental weights of

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On the Geometry of Soliton Equations,se equations may provide a better understanding of their remarkable properties. According to the geometric point of view, soliton equations are the outcome of a specific reduction process of a bi-Hamiltonian manifold. The suggestion of the paper is to pay attention also to the ‘unreduced form’ of so

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Arbitrariness of the General Solution and Symmetries, symmetry reduction. We discuss the treatment of gauge systems, especially the analysis of gauge fixing conditions. As examples, the Yang-Mills equations with the Lorentz gauge and Einstein’s vacuum field equations with harmonic coordinates are considered.

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https://doi.org/10.1007/978-3-319-65268-9erential forms and de Rham complexes are constructed. For colour differential equations, Spencer complexes are constructed. Relations between colour commutative algebras and quantizations of usual algebras are considered.

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https://doi.org/10.1007/978-981-10-7437-0manage to unify computations by reduction to the invariant systems over a homogeneous space. The conditions of coincidence of Spencer cohomologies with the cohomologies of an invariant Spencer complex we obtain from the arithmetic of a ℂ-characteristic manifold with respect to fundamental weights of the homogeneous space.

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