The Poisson Lie algebra, Rumin's complex and base change

Results from the forthcoming papers [BDK4, D3] are announced. We introduce a singular current construction, or base change, for pseudoalgebras which may be used to obtain a primitive Lie pseudoalgebra of type H from a suitable one of type K. When applied to representations, it derives the pseudo de Rham complex of type H from that of type K — which is related to Rumin’s construction from [Ru] — both with standard coefficients and with nontrivial Galois coefficients. In the latter case, the construction yields exact complexes of modules for the Poisson linearly compact Lie algebra P_2N exhibiting a nontrivial central action.