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

Abstract

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.

arXiv commentplain latex, no figures, 29 pages

References in corpus (22)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Modeling Multiple M2's
• On Foundation of the Generalized Nambu Mechanics
• Introduction to sh Lie algebras for physicists
• Three-Algebras and N=6 Chern-Simons Gauge Theories
• Comments on the Bagger-Lambert theory and multiple M2-branes
• M2-branes, 3-Lie Algebras and Plucker relations
• Classical and Quantum Nambu Mechanics
• Multiple M2-branes and Generalized 3-Lie algebras
• One-loop corrections to Bagger-Lambert theory
• Bagger-Lambert Theory for General Lie Algebras
• Higher-order simple Lie algebras
• New Generalized Poisson Structures
• The local structure of n-Poisson and n-Jacobi manifolds
• The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures
• Dynamical Symmetries and Nambu Mechanics
• Aspects of Classical and Quantum Nambu Mechanics
• On the generalizations of Poisson structures
• SDiff Gauge Theory and the M2 Condensate
• Metric 3-Lie algebras for unitary Bagger-Lambert theories
• The Z_2-graded Schouten-Nijenhuis bracket and generalized super-Poisson structures

Cited by in corpus (8)

• n-ary algebras: a review with applications
• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras
• A new approach to representations of $3$-Lie algebras and abelian extensions
• Degenerations of Filippov algebras
• Contractions of Filippov algebras
• On a class of n-Leibniz deformations of the simple Filippov algebras
• 3-Leibniz bialgebras (3-Lie bialgebras)
• Topics on n-ary algebras