Journal of Lie Theory 23 (2013), No. 1, 203--215
Copyright Heldermann Verlag 2013
Associative Forms and Second Cohomologies of Lie Superalgebras HO and KO
Jixia Yuan
School of Mathematical Sciences, Heilongjiang University, Harbin 150080, P. R. China
Wende Liu
School of Mathematical Sciences, Harbin Normal University, Harbin 150025, P. R. China
wendeliu@ustc.edu.cn
Wei Bai
School of Mathematical Sciences, Harbin Normal University, Harbin 150025, P. R. China
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.
Keywords: Lie superalgebra, associative form, cohomology.
MSC: 17B50, 17B56
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