Geodesic
Associative Forms and Second Cohomologies of Lie Superalgebras HO and KO
Jixia Yuan1 ; Wende Liu2 ; Wei Bai2, 3, 4, 5, 6
1School of Mathematical Sciences, Heilongjiang University, Harbin 150080, P. R. China
2School of Mathematical Sciences, Harbin Normal University, Harbin 150025, P. R. China
3We 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.
4Keywords: Lie superalgebra, associative form, cohomology.
5MSC: 17B50, 17B56
6[
Journal of Lie Theory, Tome 23 (2013) no. 1, pp. 203-215

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Jixia Yuan  1   ; Wende Liu  2   ; Wei Bai  2 , 3 , 4 , 5 , 6

1 School of Mathematical Sciences, Heilongjiang University, Harbin 150080, P. R. China
2 School of Mathematical Sciences, Harbin Normal University, Harbin 150025, P. R. China
3 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.
4 Keywords: Lie superalgebra, associative form, cohomology.
5 MSC: 17B50, 17B56
6 [ 
Jixia Yuan; Wende Liu; Wei 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/JOLT_2013_23_1_a10/
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     author = {Jixia Yuan and Wende Liu and Wei 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/JOLT_2013_23_1_a10/}
}
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