Lie algebra of formal vector fields which are extended by formal g-valued functions

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In this paper, we consider the infinite-dimensional Lie algebra W n ⋉ g ⊗ On 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 (gln ⊕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 WngO 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.

Original languageEnglish
Pages (from-to)2816-2830
Number of pages15
JournalJournal of Mathematical Sciences
Issue number1
StatePublished - May 2007
Externally publishedYes

Bibliographical note

Funding Information:
This research was supported by the RFBR (project 04-02-16538).

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Applied Mathematics


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