Namespaces
Variants
Actions

Poisson manifold

From Encyclopedia of Mathematics
Revision as of 09:48, 30 August 2011 by Ruiloja (talk | contribs) (Poisson manifold)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Poisson manifold

A Poisson bracket on a smooth manifold $M$ is a Lie bracket $\{~,~\}$ on the space of smooth functions $C^\infty(M)$ which, additionally, satisfies the Leibniz identity: $$ \{f,gh\}=\{f,g\}h+g\{f,h\},\qquad \forall f,g,h\in C^\infty(M).$$

How to Cite This Entry:
Poisson manifold. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Poisson_manifold&oldid=19520