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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.
##### MSC:
 17B66 Lie algebras of vector fields and related (super) algebras
##### Keywords:
Lie algebra; cochain complex; bundle; Weyl algebra; quasi-isomorphism
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