I am looking for any places in the literature where an author has had occasion to consider Poisson structures on infinitedimensional algebrogeometric objects, e.g. indvarieties or proalgebraic groups (or more specifically KacMoody groups). There are various analytic instances I know of where one can find a discussion of Poisson structures on infinitedimensional manifolds modeled on topological vector spaces, but I know of no such algebraic discussions and would be interested to hear if someone knows of circumstances where such things have come up.
