Cohomology of Filippov algebras and an analogue of Whitehead's lemma

Details Cohomology of Filippov algebras and an analogue of Whitehead's lemma Cohomology of Filippov algebras and an analogue of Whitehead's lemma

2009-05-19

arxiv.org/abs/0905.3083v1

J.Phys.Conf.Ser.175:012001,2009

Physics

Mathematical Physics

plain latex, no figures, 29 pages

Scientific paper

10.1088/1742-6596/175/1/012001

We show that two cohomological properties of semisimple Lie algebras also hold for Filippov (n-Lie) algebras, namely, that semisimple n-Lie algebras do not admit non-trivial central extensions and that they are rigid i.e., cannot be deformed in Gerstenhaber sense. This result is the analogue of Whitehead's Lemma for Filippov algebras. A few comments about the n-Leibniz algebras case are made at the end.

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