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Lie algebra of formal vector fields extended by formal \({\mathfrak g}\)-valued functions. (Russian, English) Zbl 1117.17008
Zap. Nauchn. Semin. POMI 335, 205-230 (2006); translation in J. Math. Sci., New York 143, No. 1, 2816-2830 (2007).
Let \(\mathfrak{g}\) be an arbitrary Lie algebra. The main object of study in the present paper is the Lie algebra of formal vector fields on the \(n\)-dimensional plane, extended by formal \(\mathfrak{g}\)-valued functions in \(n\) variables. The main result of the paper asserts that the cochain complex of this Lie algebra is quasi-isomorphic to the quotient of a certain Weyl algebra by a special term of standard filtration. As an application the author shows how his methods can be used in formal geometry to construct characteristic classes of bundles.
17B66 Lie algebras of vector fields and related (super) algebras
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