??try aksing about how stuff like symplectic geometry and poisson algebras (??and so forth???....) fits into theory of "dg spaces" ???...
ok, i asked, and he said that the (or at least one) idea is that a poisson structure on a space x can be thought of as a special way of taking the gca of multi-vector fields on x and putting a d on it to make it a dgca...
??so ... ??idle guess as to what sort of lie algebroid (or something...) this might correspond to ... ???maybe something about poisson manifold as foliated by symplectic manifolds... each with almost canonical connectioned line bundle, or something... ???something about getting lie algberoid fomr this, maybe ??? ....
??something about having nice simple examples to work with of lie algebroids whose representations we pretty concretely understand... ??for this purpose use those "semi-direct product algebras" ... ??"action lie algberoids" ... ?? ... including case of d-modules over an affine algebraic group ... or soemthing... and so forth... ??...
??the general program to relate lie algebroid reps to dg modules... ??something about confusion between co-simplicial vs simplicial here ???... and so forth...
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