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This article is cited in 3 scientific papers (total in 3 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.
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
Linking options:
https://www.mathnet.ru/eng/im1764https://doi.org/10.1070/IM1976v010n01ABEH001678 https://www.mathnet.ru/eng/im/v40/i1/p57
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Abstract page: | 302 | Russian version PDF: | 107 | English version PDF: | 2 | References: | 47 | First page: | 1 |
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