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

May, 2009
29 pages
Published in:
  • J.Phys.Conf.Ser. 175 (2009) 012001
e-Print:
Report number:
  • FTUV-09-0517,
  • IFIC-09-18

Citations per year

20092012201520182021012345
Abstract: (arXiv)
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.