# What is twisted in a twisted Poisson structure?

The usual definition of a twisted Poisson algebra involving a 3-form does not seem to refer to a Poisson algebra that is then twisted, i.e. twisting either the commutative product or the Lie bracket. Have I missed where such a discussion occurs?

• At @RicardoAndrade's request, I have added the tag sg.symplectic-geometry. I have also changed the tag "poissonalgebra" to "poisson-geometry". – Theo Johnson-Freyd Nov 13 '13 at 1:23

The (algebraic) Poisson counterpart of Drinfel'd twist deformation from Hopf algebras is the following: let $u$ be an invertible element of a Poisson algebra $A$. Then $A$, with the same associative multiplication but with the new bracket defined by $$[a, \, b]_u := u^{-1} [ u a, \, u b]$$ is a Poisson algebra called the u-conformal deformation of $A$. I deal with this deformation ( http://arxiv.org/abs/1406.3529 ) and seems to be quite intersting. The geometric meanning of it due by C.M. Marle (1991). A very tempting and difficult question that arise in the context is the classification of all u-conformal deformation of a given Poisson algebra.