Simplicity in the Faulkner construction
arXiv:0905.4900 · doi:10.1088/1751-8113/42/44/445206
Abstract
We revisit the Faulkner construction of metric 3-Leibniz algebras admitting an embedding Lie (super)algebra. In the case of positive-definite signature, we relate the various notions of simplicity: of the 3-algebra, of the representation and of the embedding Lie (super)algebra. This reduces their classification to the extant classifications of simple Lie (super)algebras.
12 pages. (v2: corrected an error in the proof of the third theorem. The results are unchanged.)
References in corpus (11)
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
- Gauge Symmetry and Supersymmetry of Multiple M2-Branes
- Algebraic structures on parallel M2-branes
- Modeling Multiple M2's
- On the Lie-algebraic origin of metric 3-algebras
- Multiple M2-branes and Generalized 3-Lie algebras
- The Superconformal Gaugings in Three Dimensions
- Three-algebras, triple systems and 3-graded Lie superalgebras
- Three lectures on 3-algebras
- Superconformal M2-branes and generalized Jordan triple systems
- BLG theory with generalized Jordan triple systems
Cited by in corpus (9)
- Multiple Membranes in M-theory
- Three-algebras, triple systems and 3-graded Lie superalgebras
- Symplectic Three-Algebra Unifying N=5,6 Superconformal Chern-Simons-Matter Theories
- Superspace Formulation in a Three-Algebra Approach to D=3, N=4,5 Superconformal Chern-Simons Matter Theories
- N=5 three-algebras and 5-graded Lie superalgebras
- Superalgebra Realization of the 3-algebras in N=6, 8 Chern-Simons-matter Theories
- Unexpected Features of Supersymmetry with Central Charges
- Hidden quartic symmetry in N=2 supersymmetry
- Metric 3-Leibniz algebras and M2-branes