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Abstract: Let be an algebraically closed field of characteristic 0. In this paper, we prove the equivalence between stability and quasi-reductivity for parabolic subalgebras of exceptional Lie algebras. Therefore, and considering the results of [1], we give a positive answer to the assertion (ii) of the conjecture (5.6) in [11] for parabolic Lie algebras. [Copyright &y& Elsevier]

Abstract: In this paper, we prove the following result: let X be a complex manifold, hyperbolic for the Carathéodory distance and let U be an open set relatively compact in X. Then, there exists such that we get, for the Carathéodory infinitesimal metric, . We also get results concerning fixed points of holomorphic mappings from X to U. [Copyright &y& Elsevier]

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Abstract: The fundamental example of Gerstenhaber algebra is the space of polyvector fields on , equipped with the wedge product and the Schouten bracket. In this paper, we explicitely describe what is the enveloping algebra of a Gerstenhaber algebra . This structure gives us a definition of the Chevalley–Harrison cohomology operator for . We finally show the nontriviality of a Chevalley–Harrison cohomology group for a natural Gerstenhaber subalgebra in . [Copyright &y& Elsevier]

Abstract: Let T be a closed positive current of dimension p in and H an analytic subvariety of of dimension . We denote by the slice of T in H if it exists. We consider the functions on defined by and . The aim of this paper is to establish relationship between the growth of these functions. We prove results generalizing those of L. Gruman in [Séminaire Lelong–Skoda 1981–1983, Lecture Notes in Math., vol. 1028, Springer-Verlag, Berlin, 1983, pp. 125–162] and B. Molzan, B. Shiffman and N. Sibony in [Math. Ann. 257 (1981) 43]. [Copyright &y& Elsevier]