Skip to main content
SpringerLink
Log in

Modular derivations for extensions of Poisson algebras

  • Research Article
  • Published:
Frontiers of Mathematics in China Aims and scope Submit manuscript

Abstract

We compute explicitly the modular derivations for Poisson-Ore extensions and tensor products of Poisson algebras.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ciccoli N. Poisson Ore extensions. In: Coen S, ed. Seminari di Geometria dell’Universitá di Bologna 2005–2009. 2011

  2. Dolgushev V. The Van den Bergh duality and the modular symmetry of a Poisson variety. Selecta Math, 2009, 14: 199–228

    Article  MathSciNet  MATH  Google Scholar 

  3. Huebschmann J. Duality for Lie-Rinehart algebras and the modular class. J Reine Angew Math, 1999, 510: 103–159

    MathSciNet  MATH  Google Scholar 

  4. Kontsevich M. Deformation quantization of Poisson manifolds. Lett Math Phys, 2003, 66: 157–216

    Article  MathSciNet  MATH  Google Scholar 

  5. Laurent-Gengoux C, Pichereau A, Vanhaecke P. Poisson Structures. Grundlehren Math Wiss, Vol 347. Berlin: Springer, 2013

  6. Lichnerowicz A. Les varieties de Poisson et leurs algebres de Lie associees. J Differential Geom, 1977, 12: 253–300 (in French)

    MathSciNet  MATH  Google Scholar 

  7. Luo J, Wang S-Q, Wu Q-S. Twisted Poincaré duality between Poisson homology and Poisson cohomology. J Algebra, 2015, 442: 484–505

    Article  MathSciNet  MATH  Google Scholar 

  8. Oh S Q. Poisson polynomial rings. Comm Algebra, 2006, 34: 1265–1277

    Article  MathSciNet  MATH  Google Scholar 

  9. Weibel C. An Introduction to Homological Algebra. Cambridge: Cambridge Univ Press, 1994

    Book  MATH  Google Scholar 

  10. Weinstein A. Lecture on Symplectic Manifolds. CBMS Reg Conf Ser Math, No 29. Providence: Amer Math Soc, 1977

    Google Scholar 

  11. Zhu C, Van Oystaeyen F, Zhang Y -H. On (co)homology of Frobenius Poisson algebras. J K-Theory, 2014, 14: 371–386

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

    Shengqiang Wang

Authors
  1. Shengqiang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shengqiang Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, S. Modular derivations for extensions of Poisson algebras. Front. Math. China 12, 209–218 (2017). https://doi.org/10.1007/s11464-016-0598-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11464-016-0598-8

Keywords

MSC

Search

Navigation