Journal of Generalized Lie Theory and Applications

Poisson structures on $C[X_1,... ,X_n$] associated with rigid Lie algebras

Nicolas Goze

Full-text: Open access

Abstract

We present the classical Poisson-Lichnerowicz cohomology for the Poisson algebra of polynomials $C[X_1,... ,X_n]$ using exterior calculus. After presenting some non-homogenous Poisson brackets on this algebra, we compute Poisson cohomological spaces when the Poisson structure corresponds to a bracket of a rigid Lie algebra.

Article information

Source
J. Gen. Lie Theory Appl., Volume 4 (2010), Article ID G090501, 12 pages.

Dates
First available in Project Euclid: 11 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1318365487

Digital Object Identifier
doi:10.4303/jglta/G090501

Mathematical Reviews number (MathSciNet)
MR2719413

Zentralblatt MATH identifier
1239.17018

Subjects
Primary: 17B-XX

Citation

Goze, Nicolas. Poisson structures on $C[X_1,. ,X_n$] associated with rigid Lie algebras. J. Gen. Lie Theory Appl. 4 (2010), Article ID G090501, 12 pages. doi:10.4303/jglta/G090501. https://projecteuclid.org/euclid.jglta/1318365487


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