On the structure of k-Lie algebras

Abstract

We show that the structure constants of $k$-Lie algebras, $k>3$, with a positive definite metric are the sum of the volume forms of orthogonal $k$-planes. This generalizes the result for $k=3$ in arXiv:0804.2662 and arXiv:0804.3078, and confirms a conjecture in math/0211170.

4 pages, minor changes and a reference added

References in corpus (14)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Superconformal Chern-Simons Theories
• Comments on the Bagger-Lambert theory and multiple M2-branes
• The M2-M5 Brane System and a Generalized Nahm's Equation
• Membranes on an Orbifold
• Constraining Maximally Supersymmetric Membrane Actions
• Lepton mixing angle ${\theta }_{13}=0$ with a horizontal symmetry $D_4$
• Maximally supersymmetric solutions of ten- and eleven-dimensional supergravities
• Pluecker-type relations for orthogonal planes
• Multiple M2-branes and the Embedding Tensor
• Aspects of Multiple Membranes
• Prolongations of Lie algebras and applications

Cited by in corpus (36)

• The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
• On Type IIA Penrose Limit and N=6 Chern-Simons Theories
• M2 to D2 revisited
• On M5-branes in N=6 Membrane Action
• Multiple M2-branes and Generalized 3-Lie algebras
• One-loop corrections to Bagger-Lambert theory
• An N=1 Superfield Action for M2 branes
• Multiple Membranes from Gauged Supergravity
• A New N=4 Membrane Action via Orbifold
• Janus field theories from multiple M2 branes
• Taking off the square root of Nambu-Goto action and obtaining Filippov-Lie algebra gauge theory action
• Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories
• Classification of the BPS states in Bagger-Lambert Theory
• Coulomb Branch of the Lorentzian Three Algebra Theory
• Kac-Moody Extensions of 3-Algebras and M2-branes
• Light-cone M5 and multiple M2-branes
• Holographic Supergravity Dual to Three Dimensional N=2 Gauge Theory
• Topological branes, p-algebras and generalized Nahm equations
• Lorentzian Lie n-algebras
• SDiff Gauge Theory and the M2 Condensate
• $w_{\infty }$ 3-algebra
• Towards Holographic Gravity Dual of N=1Superconformal Chern-Simons Gauge Theory
• From Simplified BLG Action to the First-Quantized M-Theory
• A note on Quantum Aspects of Multiple Membranes
• Hydrodynamics of N=6 Superconformal Chern-Simons Theories at Strong Coupling
• M-theory backgrounds with 30 Killing spinors are maximally supersymmetric
• Metric Lie n-algebras and double extensions
• D2 to M2 Procedure for D2-Brane DBI Effective Action
• Nambu-Lie 3-Algebras on Fuzzy 3-Manifolds
• On Nambu-Lie 3-algebra representations
• On thermodynamics of N=6 superconformal Chern-Simons theories at strong coupling
• Partonic description of a supersymmetric p-brane
• A note on interpreting N M2 branes
• (p+1)-Algebra for Super p-Brane: the Nambu Bracket Reformulation
• Classification of $(n+3)$-dimensional metric $n$-Lie algebras
• Exceptional Lie algebras and M-theory