## Abstract

In this paper, we consider the infinite-dimensional Lie algebra W _{n} ⋉ 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 W_{n}gO _{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 language | English |
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Pages (from-to) | 2816-2830 |

Number of pages | 15 |

Journal | Journal of Mathematical Sciences |

Volume | 143 |

Issue number | 1 |

DOIs | |

State | Published - May 2007 |

Externally published | Yes |

### 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