Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I am looking for any places in the literature where an author has had occasion to consider Poisson structures on infinite-dimensional algebro-geometric objects, e.g. ind-varieties or proalgebraic groups (or more specifically Kac-Moody groups). There are various analytic instances I know of where one can find a discussion of Poisson structures on infinite-dimensional 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.

share|cite|improve this question
Perhaps the definition of "topological coisson algebra" from Beilinson's "Remarks on topological algebras" is relevant for you. It's the definition of Poisson algebra in the setting of Tate vector spaces. – Moosbrugger Nov 8 '11 at 3:27
I should add: regular functions on a loop group naturally form a Tate space -- this is so for sufficiently nice ind-schemes (though ind-infinite type is allowed, and accounts for half of the semi-infinity of the Tate space). And the completed symmetric algebra of $\mathfrak{g}((t))$ forms a topological coisson algebra in Beilinson's sense. – Moosbrugger Nov 8 '11 at 13:43

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.