Le but de cet article est de formuler une hypothèse permettant d’affirmer que l’homologie d’une super algèbre de Lie à valeurs dans un module de dimension finie est de dimension finie
In this paper, we give an hypothesis to make sure that the homology of a Lie superalgebra operating on a finite dimensional super vector space is finite.
@article{AIF_1997__47_2_531_0, author = {Gruson, Caroline}, title = {Finitude de l'homologie de certains modules de dimension finie sur une super alg\`ebre de Lie}, journal = {Annales de l'Institut Fourier}, volume = {47}, year = {1997}, pages = {531-553}, doi = {10.5802/aif.1572}, mrnumber = {98b:17024}, zbl = {0974.17024}, language = {fr}, url = {http://dml.mathdoc.fr/item/AIF_1997__47_2_531_0} }
Gruson, Caroline. Finitude de l'homologie de certains modules de dimension finie sur une super algèbre de Lie. Annales de l'Institut Fourier, Tome 47 (1997) pp. 531-553. doi : 10.5802/aif.1572. http://gdmltest.u-ga.fr/item/AIF_1997__47_2_531_0/
[Bou] Groupes et algèbres de Lie, chap. IV, V et VI, Hermann, 1968.
,[DaKa] Polar representations, Journal of Algebra, 92 (1985), 504-524. | MR 86e:14023 | Zbl 0611.22009
and ,[Fu] Cohomology of infinite dimensional Lie algebras, Consultants Bureau, New York, 1986. | MR 88b:17001 | Zbl 0667.17005
,[FuLe] Cohomology of Lie superalgebras, Comptes Rendus de l'Académie Bulgare des Sciences, tome 37, n. 12 (1984). | MR 87e:17022 | Zbl 0586.17005
and ,[God] Topologie algébrique et théorie des faisceaux, Hermann, Paris, 1964.
,[GHV] Connections, curvature, and cohomology, Volume I, II, III. Pure and Applied Mathematics, Vol. 45, 46, 47, Academic Press, New York-London, 1976. | Zbl 0372.57001
, , ,[Ha] Algebraic geometry, GTM 52, Springer (1977). | MR 57 #3116 | Zbl 0367.14001
,[Ka1] Lie superalgebras, Advances in Math., 26 (1977), 8-96. | MR 58 #5803 | Zbl 0366.17012
,[Ka2] Some remarks on nilpotent orbits, Journal of Algebra, 64 (1980), 190-213. | MR 81i:17005 | Zbl 0431.17007
,[LuRi] A generalization of the Chevalley restriction theorem, Duke Math. J., 46 (1979), 487-496. | MR 80k:14049 | Zbl 0444.14010
and ,[MuFo] Geometric invariant theory, second edition, Ergebnisse 34, Springer (1982). | MR 86a:14006 | Zbl 0504.14008
and ,[Se] Automorphisms of simple Lie superalgebras, Math. URSS Izvestiya, vol. 24, n. 3 (1985), 539-551. | Zbl 0565.17001
,[Vu] Sur la théorie des invariants des groupes classiques, Ann. Inst. Fourier, 26-1 (1976), 1-31. | Numdam | MR 53 #8082 | Zbl 0314.20035
,[We] The Classical Groups, their Invariants and Representations, Princeton, University Press, 1946.
,