= Poisson pencil
{c}
{title2=$\Pi_\lambda=\Pi_1+\lambda\Pi_2$}
Two <Poisson structures> are compatible when every linear combination $\Pi_1+\lambda\Pi_2$ is a <Poisson structure>. This family is a Poisson pencil. In terms of the <Schouten-Nijenhuis bracket>, compatibility means $[\Pi_1,\Pi_2]=0$, in addition to the two individual <Jacobi identities>. Constant <Poisson bivectors> are compatible. Over a real <manifold>, complex parameter values refer to the complexification of its <function> algebra.
Back to article page
