6533b85afe1ef96bd12b8cb0
RESEARCH PRODUCT
Cohomology of Filippov algebras and an analogue of Whitehead's lemma
J. A. De AzcárragaJosé M. Izquierdosubject
High Energy Physics - TheoryHistoryLemma (mathematics)Pure mathematicsMathematics::Dynamical SystemsMathematics::Rings and AlgebrasFOS: Physical sciencesMathematical Physics (math-ph)Mathematics - Rings and AlgebrasMathematics::Algebraic TopologyCohomologyComputer Science ApplicationsEducationHigh Energy Physics - Theory (hep-th)Rings and Algebras (math.RA)Mathematics::K-Theory and HomologyWhitehead's lemmaMathematics::Quantum AlgebraLie algebraFOS: MathematicsMathematical PhysicsMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-05-19 | Journal of Physics: Conference Series |