Root systems for Lorentzian Kac–Moody algebras in rank 3

DOI10.1112/blms/bdv007zbMath1378.17022arXiv1209.0022OpenAlexW3103670676MaRDI QIDQ5245497

Daniel Allcock

Publication date: 8 April 2015

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.0022

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Root systems (17B22)

Related Items

Apollonian packings and Kac-Moody root systems ⋮ Arithmetic hyperbolic reflection groups

Cites Work

• Unnamed Item
• Unnamed Item
• On the maximal dimension of Lorentz lattices with cofinite reflection group
• The monster Lie algebra
• A theory of Lorentzian Kac-Moody algebras
• Automorphic forms with singularities on Grassmannians
• A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2
• Monstrous moonshine and monstrous Lie superalgebras
• \(K3\) surfaces, Lorentzian Kac-Moody algebras and mirror symmetry
• Infinitely many hyperbolic Coxeter groups through dimension 19.
• Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras
• Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits
• AUTOMORPHIC FORMS AND LORENTZIAN KAC–MOODY ALGEBRAS PART I
• AUTOMORPHIC FORMS AND LORENTZIAN KAC–MOODY ALGEBRAS PART II
• Igusa modular forms and 'the simplest' Lorentzian Kac-Moody algebras
• Reflection groups in Lobachevskii spaces and the denominator identity for Lorentzian Kac-Moody algebras
• On classification of Lorentzian Kac-Moody algebras
• BASIS OF THE DIAGRAM METHOD FOR GENERALIZED REFLECTION GROUPS IN LOBACHEVSKY SPACES AND ALGEBRAIC SURFACES WITH NEF ANTICANONICAL CLASS
• Dynkin diagrams for hyperbolic Kac-Moody algebras
• Lie algebras associated with generalized Cartan matrices