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

J A de Azcárraga, J M Izquierdo
2009 Journal of Physics, Conference Series  
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.
doi:10.1088/1742-6596/175/1/012001 fatcat:dptgwf5l4narrnetuhchues33y