On Nambu-Lie 3-algebra representations

Abstract

We propose a recipe to construct matrix representations of Nambu--Lie 3-algebras in terms of irreducible representations of underlying Lie algebra. The case of Euclidean four-dimensional 3-algebra is considered in details. We find that representations of this 3-algebra are not possible in terms of only Hermitian matrices in spite of its Euclidean nature.

10 pages, no figures, bibliography updated, some typo(s) corrected

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• $w_{\infty }$ 3-algebra
• Towards Holographic Gravity Dual of N=1Superconformal Chern-Simons Gauge Theory
• Relaxed Three-Algebras: Their Matrix Representations and Implications for Multi M2-brane Theory
• Hydrodynamics of N=6 Superconformal Chern-Simons Theories at Strong Coupling
• Bagger-Lambert theory on an orbifold and its relation to Chern-Simons-matter theories
• On thermodynamics of N=6 superconformal Chern-Simons theories at strong coupling
• (p+1)-Algebra for Super p-Brane: the Nambu Bracket Reformulation
• The infinite dimensional Unital 3-Lie Poisson algebra