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- W2000353211 abstract "Let M be a smooth manifold, and 2l(M) the Lie algebra of all smooth vector fields on M. Assume that M admits a volume form T, a symplectic form CD or a contact form 9. Then we have natural Lie subalgebras of 2l(M) as 21T(M), 2l;(M), 9IW(M), 2l;o(M), 210(M) (see §1.1). These Lie algebras including 2l(M) itself are called of classical type. Here we are interested in the cohomology ff*(2l; 21) of the Lie algebra 21 with coefficients in its adjoint representation. Calculations of them are not easy in general. But the first cohomology can be calculated rather easily since H *(2J; 21) is interpreted in terms of derivations of 21. From this point of view F. Takens [5] calculated ff ^(M); $l(M)) in 1973. Later A. Avez-A. LichnerowiczA. Diaz-Miranda [2] and the author [3] calculated HWm(M) 2IW(M)) of Lie algebra 2IW(M) of hamiltonian vector fields by different methods. In the present paper, we will calculate H(2l; 21) for all 21 of classical type. Our results can be summarized as follows." @default.
- W2000353211 created "2016-06-24" @default.
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- W2000353211 date "1975-01-01" @default.
- W2000353211 modified "2023-09-27" @default.
- W2000353211 title "Cohomologies of Lie algebras of vector fields with coefficients in adjoint representations case of classical type" @default.
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- W2000353211 doi "https://doi.org/10.2977/prims/1195191693" @default.
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