Geodesic
Associative Forms and Second Cohomologies of Lie Superalgebras HO and KO
Journal of Lie theory, Tome 23 (2013) no. 1, pp. 203-215 Cet article a éte moissonné depuis la source Heldermann Verlag

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We consider two families of finite-dimensional simple Lie superalgebras of Cartan type, denoted by HO and KO, over an algebraically closed field of characteristic p > 3 . Using the weight space decompositions and the principal gradings we first show that neither HO nor KO possesses a nondegenerate associative form. Then, by means of computing the superderivations from the Lie superalgebras under consideration into their dual modules, the second cohomology groups with coefficients in the trivial modules are proved to be vanishing.
Classification : 17B50, 17B56
Mots-clés : Lie superalgebra, associative form, cohomology 
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     author = {J. Yuan and W. Liu and W. Bai },
     title = {Associative {Forms} and {Second} {Cohomologies} of {Lie} {Superalgebras} {HO} and {KO}},
     journal = {Journal of Lie theory},
     pages = {203--215},
     year = {2013},
     volume = {23},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2013_23_1_JLT_2013_23_1_a10/}
}
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J. Yuan; W. Liu; W. Bai . Associative Forms and Second Cohomologies of Lie Superalgebras HO and KO. Journal of Lie theory, Tome 23 (2013) no. 1, pp. 203-215. http://geodesic.mathdoc.fr/item/JLT_2013_23_1_JLT_2013_23_1_a10/