Poncin, Norbert On the cohomology of the Nijenhuis-Richardson graded Lie algebra of the space of functions of a manifold. (English) Zbl 1012.17014 J. Algebra 243, No. 1, 16-40 (2001). This is a full proof of results presented by the author in [Bull. Belg. Math. Soc. – Simon Stevin 8, No. 1, 141-146 (2001; Zbl 0989.17012)] about low-dimensional cohomology of the Nijenhuis-Richardson graded Lie algebra of the space of functions on a manifold, with coefficients in an adjoint module. Reviewer: Pasha Zusmanovich (Amsterdam) Cited in 2 Documents MSC: 17B56 Cohomology of Lie (super)algebras 17B66 Lie algebras of vector fields and related (super) algebras Keywords:Nijenhuis-Richardson Lie algebra; Lie algebra cohomology; de Rham cohomology Citations:Zbl 0989.17012 PDFBibTeX XMLCite \textit{N. Poncin}, J. Algebra 243, No. 1, 16--40 (2001; Zbl 1012.17014) Full Text: DOI References: [1] Bayen, F.; Flato, M.; Fronsdal, C.; Lichnerowicz, A.; Sternheimer, D., Deformation theory and quantization, Ann. Phys., 111, 61-110 (1978) · Zbl 0377.53024 [2] Wilde, M. De; Lecomte, P. B.A., Formal deformations of the Poisson Lie algebra of a symplectic manifold and star-products: Existence, equivalence, derivations, NATO ASI Ser. C (1988), Kluwer Academic: Kluwer Academic Dordrecht, p. 897-960 [3] M. Kontsevich, Deformation quantization of Poisson manifolds, preprint, IHES, 1997.; M. Kontsevich, Deformation quantization of Poisson manifolds, preprint, IHES, 1997. [4] Lecomte, P. B.A.; Melotte, D.; Roger, C., Explicit form and convergence of 1-differential formal deformations of the Poisson Lie algebra, Lett. Math. Phys., 18, 275-285 (1989) · Zbl 0685.17012 [5] Nijenhuis, A.; Richardson, R., Deformation of Lie algebra structures, J. Math. Mech., 17, 89-105 (1967) · Zbl 0166.30202 [6] Peetre, J., Une caractérisation abstraite des opérateurs différentiels, Math. Scand., 7, 211-218 (1959) · Zbl 0089.32502 [7] Poncin, N., Premier et deuxième espaces de cohomologie de l’algèbre de Lie des opérateurs différentiels sur une variété, à coefficients dans les fonctions, Bull. Soc. Roy. Sci. Liège, 67, 291-337 (1998) · Zbl 0971.17011 [8] Poncin, N., Troisième espace de cohomologie de l’algèbre de Lie des opérateurs différentiels sur une variété, à coefficients dans les fonctions, Bull. Soc. Roy. Sci. Liège, 67, 339-393 (1998) · Zbl 0971.17012 [9] Poncin, N., Cohomologie de Chevalley-Eilenberg de l’algèbre des opérateurs locaux sur I’espace des fonctions d’une variété, Publ. Centre Univ. Luxembourg Trav. Math., 10, 103-115 (1998) · Zbl 0951.17010 [10] Poncin, N., Cohomologie de l’algèbre de Lie des opérateurs différentiels sur une variété, à coefficients dans les fonctions, C.R. Acad. Sci. Paris Sér. I, 328, 789-794 (1999) · Zbl 0968.17008 [11] Weyl, H., The Classical Groups, Their Invariants and Representations. The Classical Groups, Their Invariants and Representations, Princeton Math. Ser. (1946), Princeton Univ. Press: Princeton Univ. Press Princeton · Zbl 1024.20502 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.