Dans le présent article, nous déterminons, pour chaque variété parallélisable compacte lisse
In the present paper we determine for each parallelizable smooth compact manifold
Keywords: Lie algebra of vector fields, Lie algebra cohomology, Gelfand-Fuks cohomology, extended affine Lie algebra
Mot clés : algèbre de Lie des champs vectoriels, cohomologie de l’algèbre de Lie, cohomologie de Gelfand-Fuks, algèbre de Lie affine étendu
@article{AIF_2008__58_6_1937_0, author = {Billig, Yuly and Neeb, Karl-Hermann}, title = {On the cohomology of vector fields on parallelizable manifolds}, journal = {Annales de l'Institut Fourier}, pages = {1937--1982}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {6}, year = {2008}, doi = {10.5802/aif.2402}, zbl = {1157.17007}, mrnumber = {2473625}, language = {en}, url = {https://www.numdam.org/articles/10.5802/aif.2402/} }
TY - JOUR AU - Billig, Yuly AU - Neeb, Karl-Hermann TI - On the cohomology of vector fields on parallelizable manifolds JO - Annales de l'Institut Fourier PY - 2008 SP - 1937 EP - 1982 VL - 58 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://www.numdam.org/articles/10.5802/aif.2402/ DO - 10.5802/aif.2402 LA - en ID - AIF_2008__58_6_1937_0 ER -
%0 Journal Article %A Billig, Yuly %A Neeb, Karl-Hermann %T On the cohomology of vector fields on parallelizable manifolds %J Annales de l'Institut Fourier %D 2008 %P 1937-1982 %V 58 %N 6 %I Association des Annales de l’institut Fourier %U https://www.numdam.org/articles/10.5802/aif.2402/ %R 10.5802/aif.2402 %G en %F AIF_2008__58_6_1937_0
Billig, Yuly; Neeb, Karl-Hermann. On the cohomology of vector fields on parallelizable manifolds. Annales de l'Institut Fourier, Tome 58 (2008) no. 6, pp. 1937-1982. doi : 10.5802/aif.2402. https://www.numdam.org/articles/10.5802/aif.2402/
[1] Manifolds, Tensor Analysis, and Applications, Addison-Wesley, 1983 | MR | Zbl
[2] Realizations of graded-simple algebras as loop algebras (math.RA/0511723)
[3] Infinite-dimensional Lie superalgebras, Walter de Gruyter & Co, 1992 | MR | Zbl
[4] The de Rham complex on infinite dimensional manifolds, Quart. J. Math. Oxford, Volume 38 (1987) no. 2, pp. 131-154 | DOI | MR | Zbl
[5] The centroid of extended affine and root graded Lie algebras, J. Pure Appl. Algebra, Volume 205 (2006) no. 1, pp. 117-145 | DOI | MR
[6] Irreducible representations for toroidal Lie algebras, J. Algebra, Volume 221 (1999), pp. 188-231 | DOI | MR | Zbl
[7] Homogeneous spaces of infinitedimensional Lie algebras and characteristic classes of foliations, Russ. Math. Surveys, Volume 28 (1973) no. 4, pp. 107-142 | DOI | Zbl
[8] A category of modules for the full toroidal Lie algebra, Int. Math. Res. Not., 2006 (Art. ID 68395, 46 pp.) | MR
[9] Cohomology theory of Lie groups and Lie algebras, Transactions of the Amer. Math. Soc., Volume 63 (1948), pp. 85-124 | DOI | MR | Zbl
[10] Computations of Gelfand-Fuks cohomology, the cohomology of function spaces, and the cohomology of configuration spaces, Geometric applications of homotopy theory I (Lectures Notes Math.), Volume 657, Proc. Conf. Evanston, Ill (1978), pp. 106-173 | MR | Zbl
[11] Cohomology of the Lie algebra of smooth vector fields of a manifold, associated to the Lie derivative of smooth forms, J. Math. Pures et Appl., Volume 62 (1983), pp. 197-214 | MR | Zbl
[12] Vertex representations for
[13] Cohomologies of Lie Groups and Lie Algebras, Lie Groups and Lie Algebras II (Encyclop. Math. Sci.), Volume 21, Springer-Verlag (2001) | Zbl
[14] Cohomologie des représentations définies par la dérivation de Lie et à valeurs dans les formes, de l’algèbre de Lie des champs de vecteurs d’une variété différentiable. Premiers espaces de cohomologie. Applications, C. R. Acad. Sci. Paris, Sér. A-B, Volume 291 (1980) no. 4, p. A331-A335 | Zbl
[15] Cohomology of Infinite-Dimensional Lie Algebras, Consultants Bureau, New York, London, 1986 | MR | Zbl
[16] Cohomology of the Lie algebra of formal vector fields, Izv. Akad. Nauk SSSR (1970) no. 34, pp. 322-337 | MR | Zbl
[17] Cohomology of the Lie algebra of vector fields with nontrivial coefficients, Func. Anal. and its Appl., Volume 4 (1970), pp. 181-192 | DOI | MR | Zbl
[18] Cohomologies d’algèbres de Lie de champs de vecteurs formels, Séminaire Bourbaki (1972/1973), Exp. No. 421 (Lecture Notes in Math.), Volume 383 (1974), pp. 69-87 | Numdam | Zbl
[19] Sur la cohomologie de l’algèbre de Lie des champs de vecteurs, Ann. Sci. Ec. Norm. Sup., 4e série, Volume 9 (1976), pp. 503-532 | Numdam | Zbl
[20] Cohomology of Lie algebras, Annals of Math., Volume 57 (1953) no. 3, pp. 591-603 | DOI | MR | Zbl
[21] Kähler differentials and coverings of complex simple Lie algebras extended over a commutative ring, J. Pure Applied Algebra, Volume 34 (1984), pp. 265-275 | DOI | MR | Zbl
[22] Homologie des complexes de formes différentielles d’ordre supérieur, Collection of articles dedicated to Henri Cartan on the occasion of his 70th birthday, I, Volume 7, Ann. Sci. École Norm. Sup. (4) (1974), pp. 139-153 | Numdam | Zbl
[23] Lowest-energy representations of non-centrally extended diffeomorphism algebras, Comm. Math. Phys., Volume 201 (1999), pp. 461-470 | DOI | MR | Zbl
[24] Central extensions of topological current algebras, Geometry and Analysis on Finite- and Infinite-Dimensional Lie Groups, Volume 55, Banach Center Publications, Warszawa (2002), pp. 61-76 | MR | Zbl
[25] Abelian extensions of infinite-dimensional Lie groups, Travaux mathématiques, Volume 15 (2004), pp. 69-194 | MR | Zbl
[26] Lie algebra extensions and higher order cocycles, J. Geom. Sym. Phys., Volume 5 (2006), pp. 48-74 | MR | Zbl
[27] Non-abelian extensions of topological Lie algebras, Communications in Algebra, Volume 34 (2006), pp. 991-1041 | DOI | MR
[28] Extended affine Lie algebras, C. R. Math. Acad. Sci. Soc. R. Can., Volume 26 (2004) no. 3, pp. 90-96 | MR | Zbl
[29] Loop Groups, Oxford University Press, Oxford, 1986 | MR | Zbl
[30] Cohomology of certain infinite-dimensional Lie algebras, Funct. Anal. Appl., Volume 13 (1971), pp. 340-342 | Zbl
[31] On the continuous cohomology of the Lie algebra of vector fields, Proc. Jap. Math. Soc., Volume 53:A (1977), pp. 134-138 | MR | Zbl
[32] Continuous cohomology of the Lie algebra of vector fields, Memoirs of the Amer. Math. Soc., Volume 253 (1981) no. 34, pp. 154p. | MR | Zbl
- Crossed morphisms, integration of post-Lie algebras and the post-Lie Magnus expansion, Communications in Algebra, Volume 49 (2021) no. 8, p. 3507 | DOI:10.1080/00927872.2021.1900212
- Lie Groups of Bundle Automorphisms and Their Extensions, Developments and Trends in Infinite-Dimensional Lie Theory, Volume 288 (2011), p. 281 | DOI:10.1007/978-0-8176-4741-4_9
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