2003/04/30 by F. Englert, François Englert, Laurent Houart +5 · 7 citations
Mathematics · Physics and Astronomy · #Affine Lie algebra #Algebra over a field #Automorphism #Black Holes and Theoretical Physics #Cartan subalgebra #Cosmology and Gravitation Theories #Current algebra #Diagonal #Homogeneous space #Lie algebra #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Philosophy #Physics #Pure mathematics #Simple (philosophy) #String (physics) #String theory #Subalgebra #Superstring theory #Supersymmetry #Symmetry (geometry) #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1088/1126-6708/2003/09/020
published as JHEP 0309:020,2003 · Latex 41 pages, 2 figures. Introduction modified (and references renumbered) for better focusing. Minor changes in the bulk. Two references added
openalex publication_date 2003/09/08 · arxiv created 2003/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the Cartan subalgebra of any very extended algebra G+++ where G is a simple Lie algebra and let the parameters be space-time fields. These are identified with diagonal metrics and dilatons. Using the properties of the algebra, we find that for all very extensions G+++ of simple Lie algebras there are theories of gravity and matter, which admit classical solutions carrying representations of the Weyl group of G+++. We also identify the T and S-dualities of superstrings and of the bosonic string with Weyl reflections and outer automorphisms of well-chosen very extended algebras and we exhibit specific features of the very extensions. We take these results as indication that very extended algebras underlie symmetries of any consistent theory of gravity and matter, and might encode basic information for the construction of such theory.