
Journal of Lie Theory 23 (2013), No. 1, 203215 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 finitedimensional 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 [ Fulltextpdf (344 KB)] for subscribers only. 