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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 1, Pages 57–64 (Mi izv1764)  

This article is cited in 2 scientific papers (total in 2 papers)

Finite-dimensional Lie algebras of formal vector fields and characteristic classes of homogeneous foliations

D. B. Fuchs


Abstract: In [5], I. M. Gel'fand and the author computed the cohomology of the Lie algebra $W_n$ of formal vector fields in $n$-dimensional space. The present article is devoted to the study of homomorphisms $H^*(W_n;\mathbf R)\to H^*(\mathfrak g;\mathbf R)$ induced by imbeddings of finite-dimensional subalgebras in $W_n$. We show that there exist elements of $H^*(W_n;\mathbf R)$ which are annihilated by any such homomorphism. On the other hand, we show that the image of the cohomology homomorphism induced by the well-known embedding $\mathfrak{sl}(n+1,\mathbf R)\to W_n$ has dimension $2^{n-1}+1$. The results are applied to characteristic classes of foliations.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:1, 55–62

Bibliographic databases:

UDC: 519.4
MSC: 57D25, 17B60, 57D20, 57D30
Received: 16.01.1975

Citation: D. B. Fuchs, “Finite-dimensional Lie algebras of formal vector fields and characteristic classes of homogeneous foliations”, Izv. Akad. Nauk SSSR Ser. Mat., 40:1 (1976), 57–64; Math. USSR-Izv., 10:1 (1976), 55–62

Citation in format AMSBIB
\Bibitem{Fuc76}
\by D.~B.~Fuchs
\paper Finite-dimensional Lie algebras of formal vector fields and characteristic classes of homogeneous foliations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 1
\pages 57--64
\mathnet{http://mi.mathnet.ru/izv1764}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=413125}
\zmath{https://zbmath.org/?q=an:0336.57016}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 1
\pages 55--62
\crossref{https://doi.org/10.1070/IM1976v010n01ABEH001678}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. L. Tabachnikov, “On characteristic classes of homogeneous foliations”, Russian Math. Surveys, 39:2 (1984), 203–204  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. S. L. Tabachnikov, “Characteristic classes of Grassmanian bundles”, Funct. Anal. Appl., 19:1 (1985), 71–72  mathnet  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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