A class of Lorentzian Kac-Moody algebras

Abstract

We consider a natural generalisation of the class of hyperbolic Kac-Moody algebras. We describe in detail the conditions under which these algebras are Lorentzian. We also construct their fundamental weights, and analyse whether they possess a real principal so(1,2) subalgebra. Our class of algebras include the Lorentzian Kac-Moody algebras that have recently been proposed as symmetries of M-theory and the closed bosonic string.

40 pages TeX, 5 eps-figures

Cited by in corpus (70)

• $E_{11}$, SL(32) and Central Charges
• The E_{11} origin of all maximal supergravities
• Duality Invariant Actions and Generalised Geometry
• Very-extended Kac-Moody algebras and their interpretation at low levels
• Spacelike Singularities and Hidden Symmetries of Gravity
• The IIA, IIB and eleven dimensional theories and their common E_{11} origin
• The Symmetry of M-Theories
• G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions
• Representations of G+++ and the role of space-time
• E_{11} origin of Brane charges and U-duality multiplets
• String Solitons and T-duality
• E10 and SO(9,9) invariant supergravity
• Dual fields and E_{11}
• G+++ Invariant Formulation of Gravity and M-Theories: Exact Intersecting Brane Solutions
• An E9 multiplet of BPS states
• The tensor hierarchy algebra
• Charge multiplets and masses for E(11)
• Hidden Symmetries and Dirac Fermions
• Enhanced Coset Symmetries and Higher Derivative Corrections
• Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories
• E_{11}, ten forms and supergravity
• Geometric Configurations, Regular Subalgebras of E10 and M-Theory Cosmology
• Real forms of very extended Kac-Moody algebras and theories with eight supersymmetries
• G+++ and Brane Solutions
• Perturbation Theory From Automorphic Forms
• Intersection rules, dynamics and symmetries
• Constraints on Automorphic Forms of Higher Derivative Terms from Compactification
• Duality Symmetries and G^{+++} Theories
• E11 as E10 representation at low levels
• E11 and Supersymmetry
• Dualities and signatures of G++ invariant theories
• Borcherds Algebras and N=4 Topological Amplitudes
• Arithmetic and Hyperbolic Structures in String Theory
• Poincare Duality and G+++ algebra's
• Pure type I supergravity and DE(10)
• Real forms of extended Kac-Moody symmetries and higher spin gauge theories
• Kac-Moody Algebras in M-theory
• E11 and Spheric Vacuum Solutions of Eleven- and Ten dimensional Supergravity Theories
• Sugawara-type constraints in hyperbolic coset models
• Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
• Higher derivative type II string effective actions, automorphic forms and E11
• An overview of generalised Kac-Moody algebras on compact real manifolds
• Gravity, Dual Gravity and A1+++
• Hidden Symmetry Unmasked: Matrix Theory and E(11)
• Duality-Symmetric Approach to General Relativity and Supergravity
• Standard and Non-standard Extensions of Lie algebras
• Higher spin fields from indefinite Kac-Moody algebras
• On Brane Solutions Related to Non-Singular Kac-Moody Algebras
• Lorentzian Toda field theories
• Some simple predictions from E_{11} symmetry
• Parameters, limits and higher derivative type II string corrections
• The emergence of fermions and the E11 content
• Black brane solutions related to non-singular Kac-Moody algebras
• Infinite affine, hyperbolic and Lorentzian Weyl groups with their associated Calogero models
• Connections between Kac-Moody algebras and M-theory
• Hyperbolic Invariance in Type II Superstrings
• Poisson equations, higher derivative automorphic forms and string parameter limits
• On the structure of Kac-Moody algebras
• N-Extended Lorentzian Kac-Moody algebras
• On the sigma-model structure of type IIA supergravity action in doubled field approach
• Hidden Symmetries of M-Theory and Its Dynamical Realization
• Non-linear parent action and dual N=1 D=4 supergravity
• Algebraic structures in M-theory
• Gravitational Billiards, Dualities and Hidden Symmetries
• From brane dynamics to a Kac-Moody invariant formulation of M-theories
• Monstrous M-theory
• Diagrammar and metamorphosis of coset symmetries in dimensionally reduced type IIB supergravity
• ${\mathfrak{sl}}_2$ triples whose nilpositive elements are in a space which is spanned by the real root vectors in rank 2 symmetric hyperbolic Kac-Moody Lie algebras
• A Calogero Model with root string representatives of infinite order Coxeter orbits
• Toda field theories and Calogero models associated to infinite Weyl groups