Tokyo Journal of Mathematics

The Cohomology of the Lie Algebras of Formal Poisson Vector Fields and Laplace Operators

Masashi TAKAMURA

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Abstract

We review a Laplace operator on the cochain complex of the Lie algebra of the formal Poisson vector fields to obtain an analogy of the Hodge theorem for its cohomology. We present intermediate results of the computation on the plane.

Article information

Source
Tokyo J. Math., Volume 32, Number 1 (2009), 105-111.

Dates
First available in Project Euclid: 7 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1249648412

Digital Object Identifier
doi:10.3836/tjm/1249648412

Mathematical Reviews number (MathSciNet)
MR2541157

Zentralblatt MATH identifier
1248.17018

Subjects
Primary: 17B66: Lie algebras of vector fields and related (super) algebras
Secondary: 17B56: Cohomology of Lie (super)algebras

Citation

TAKAMURA, Masashi. The Cohomology of the Lie Algebras of Formal Poisson Vector Fields and Laplace Operators. Tokyo J. Math. 32 (2009), no. 1, 105--111. doi:10.3836/tjm/1249648412. https://projecteuclid.org/euclid.tjm/1249648412


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References

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