Lie algebra of formal vector fields which are extended by formal g-valued functions |
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Authors: | A S Khoroshkin |
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Institution: | (1) St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia |
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Abstract: | In this paper, we consider the infinite-dimensional Lie algebra Wn⋉g⊗O
n of formal vector fields on the n-dimensional plane which is extended by formal g-valued functions of n variables. Here g is an arbitrary Lie algebra. We show that the cochain complex of this Lie algebra is quasi-isomorphic to the quotient of
the Weyl algebra of (gl
n ⊕ g) by the (2n+1)st term of the standard filtration. We consider separately the case of a reductive Lie algebra g. We show how one can use the methods of formal geometry to construct characteristic classes of bundles. For every G-bundle on an n-dimensional complex manifold, we construct a natural homomorphism from the ring A of relative cohomologies
of the Lie algebra Wn⋉g⊗O
n to the ring of cohomologies of the manifold. We show that generators of the ring A are mapped under this homomorphism to
characteristic classes of tangent and G-bundles. Bibliography: 10 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 335, 2006, pp. 205–230. |
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Keywords: | |
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