Associative forms and second cohomologies of Lie superalgebras $HO$ and $KO$

Details Associative forms and second cohomologies of Lie superalgebras $HO$ and $KO$ Associative forms and second cohomologies of Lie superalgebras $HO$ and $KO$

2009-11-18

arxiv.org/abs/0911.3468v1

Mathematics

Rings and Algebras

15 pages

Scientific paper

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 in consideration into their dual modules, the second cohomology groups with coefficients in the trivial modules are proved to be vanishing.

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