Skip to main content
Log in

Poisson structures associated with algebras of differential operators

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

For differential operators forming an algebra of a certain class that includes algebras of higher derivatives, a Poisson structure is introduced and the first term of the Hochschild spectral sequence is calculated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J.-L. Brylinski, “A differential complex for Poisson manifolds,”J. Differential Geom.,28, 93–114 (1988).

    MATH  MathSciNet  Google Scholar 

  2. G. Hochschild, B. Kostant, and A. Rosenberg, “Differential forms on regular affine algebras,”Trans. Am. Math. Soc.,102, 383–408 (1962).

    MathSciNet  Google Scholar 

  3. A. M. Vinogradov, I. S. Krasil'shchik, and V. V. Lychagin,Introduction to the Geometry of Nonlinear Differential Equations [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  4. H. Cartan and S. Eilenberg,Homological Algebra, Princeton Univ. Press, Princeton (1956).

    Google Scholar 

  5. O. V. Lychagina, “The spectral sequence for the Hochschild homology of the algebra of higher derivations,”Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.],3, 18–22 (1993).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated fromMatematicheskie Zametki, Vol. 58, No. 2, pp. 256–271, August, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lychagina, O.V. Poisson structures associated with algebras of differential operators. Math Notes 58, 850–860 (1995). https://doi.org/10.1007/BF02304107

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02304107

Keywords

Navigation