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Spencer cohomologies and symmetry groups

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Abstract

We propose the construction of a spectral sequence converging to Spencer cohomologies. By using symmetry groups of differential equations systems, we 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 the homogeneous space.

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References

  1. Spencer, D. C.: Overdetermined systems of linear partial differential equations,Bull. Amer. Math. Soc. 75(2) (1969), 179–239.

    Google Scholar 

  2. Quillen, D. G.: Formal properties of Overdetermined systems of linear partial differential equations, Thesis, Harvard University, Cambridge, Mass., 1964, p. 96.

    Google Scholar 

  3. Kuranishi, M.: On E. Cartan's prolongations theorem of exterior differential systems,Amer. J. Math. 79(1) (1957), 1–47.

    Google Scholar 

  4. Goldshmidt, H.: Existence theorems for analytic linear partial differential equations,Ann. Math. 86(2) (1967), 246–270.

    Google Scholar 

  5. Guillemin, V.: Some algebraic results concerning the characteristics of Overdetermined partial differential equations,Amer. J. Math. 90 (1968), 270–284.

    Google Scholar 

  6. Lychagin, V. V. and Zil'bergleit, L. V.: Spencer cohomology of differential equations, inLecture Notes in Math. 1453, Springer-Verlag, Berlin, 1990, pp. 121–136.

    Google Scholar 

  7. Lychagin, V. V.: Differential operators on fiber bundles,Uspekhi Mat. Nauk 40(2) (1985), 187–188 (in Russian);Russian Math. Surveys 40 (1985).

    Google Scholar 

  8. Lychagin, V. V. and Zil'bergleit, L. V.: Spencer cohomologies of invariant systems of differential equations above homogeneous spaces,Russian Math. Dokl. 328(5) (1992), 544–546 (in Russian).

    Google Scholar 

  9. Bourbaki, N.:Algèbre. Chap. X, Algèbre homologique, Masson, Paris, 1980, p. 192.

    Google Scholar 

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Authors and Affiliations

  1. “Sophus Lie” Centre(Moscow Branch), PB 546, 119618, Moscow, Russia

    V. Lychagin & L. Zil'bergleit

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  1. V. Lychagin
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  2. L. Zil'bergleit
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Lychagin, V., Zil'bergleit, L. Spencer cohomologies and symmetry groups. Acta Appl Math 41, 227–245 (1995). https://doi.org/10.1007/BF00996114

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  • DOI: https://doi.org/10.1007/BF00996114

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