2008/06/19 by Paul de Medeiros, José Figueroa-O'Farrill, Elena Méndez-Escobar · 2 citations
Mathematics · Physics and Astronomy · #Adjoint representation #Adjoint representation of a Lie algebra #Advanced Topics in Algebra #Fundamental representation #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Killing form #Lie conformal algebra #Lie group #Representation of a Lie group #Simple Lie group #hep-th #math.RT
paper · pdf · doi:10.1088/1126-6708/2008/08/045
published as JHEP 0808:045,2008 · 38 pages
arxiv created 2008/06/19 · openalex publication_date 2008/08/13 · arxiv updated 2011/06/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We recast physical properties of the Bagger-Lambert theory, such as shift-symmetry and decoupling of ghosts, the absence of scale and parity invariance, in Lie 3-algebraic terms, thus motivating the study of metric Lie 3-algebras and their Lie algebras of derivations. We prove a structure theorem for metric Lie 3-algebras in arbitrary signature showing that they can be constructed out of the simple and one-dimensional Lie 3-algebras iterating two constructions: orthogonal direct sum and a new construction called a double extension, by analogy with the similar construction for Lie algebras. We classify metric Lie 3-algebras of signature (2,p) and study their Lie algebras of derivations, including those which preserve the conformal class of the inner product. We revisit the 3-algebraic criteria spelt out at the start of the paper and select those algebras with signature (2,p) which satisfy them, as well as indicate the construction of more general metric Lie 3-algebras satisfying the ghost-decoupling criterion.