Complete filtered Lie algebras and the Spencer cohomology (Q1262936)

Let \(L\) be a complete filtered Lie algebra and \(G_ L=\prod G_ p\) \((p\geq -1)\) its associated graded algebra [see \textit{V. Guillemin} and \textit{S. Sternberg}, Bull. Am. Math. Soc. 70, 16--47 (1964; Zbl 0121.38801), and \textit{S. Kobayashi} and \textit{T. Nagano}, ``On filtered Lie algebras and geometric structures, I--IV, J. Math. Mech. 13, 875--907 (1964; Zbl 0142.19504)]; 14, 513--521; 679--706; 15, 163--175 (1965; Zbl 0163.28103)]. It is known that \(G_ L\approx L\) if certain Spencer cohomology groups vanish. In this paper, the author generalizes these results by showing that one can often define certain elements in \(H^{i,j}(\prod G_ p)\) which determine (up to an isomorphism) all complete filtered Lie algebras \(L\) with the graded algebra \(G_ L\cong \prod G_ p\).