Dynkin diagrams for hyperbolic Kac-Moody algebras
- 21 September 1989
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 22 (18) , 3753-3769
- https://doi.org/10.1088/0305-4470/22/18/015
Abstract
Hyperbolic algebras such as E10 are based on Minkowskian root spaces that revert to finite or affine root systems upon the removal of any simple root. In string theory terms, finite Lie, affine Kac-Moody and hyperbolic Kac-Moody algebras are generated by tachyon vertex operators, trachyon plus photon vertex operators, and vertex operators for all mass levels, respectively. The 136 possible hyperbolic Dynkin diagrams between the ranks 3 and 10 are classified and exhibited, completing an earlier enumeration by Kac of the 18 rank 7-10 cases. The rank-2 hyperbolic algebras, infinite in number, have been classified by Lepowsky and Moody (1979).Keywords
This publication has 10 references indexed in Scilit:
- KAC-MOODY AND VIRASORO ALGEBRAS IN RELATION TO QUANTUM PHYSICSInternational Journal of Modern Physics A, 1986
- TOPOLOGICAL TOOLS IN 10-DIMENSIONAL PHYSICSInternational Journal of Modern Physics A, 1986
- Unitary representations of some infinite dimensional groupsCommunications in Mathematical Physics, 1981
- Basic representations of affine Lie algebras and dual resonance modelsInventiones Mathematicae, 1980
- Root systems of hyperbolic typeAdvances in Mathematics, 1979
- Hyperbolic Lie algebras and quasi-regular cusps on Hilbert modular surfacesMathematische Annalen, 1979
- THE WEYL GROUP OF A GRADED LIE ALGEBRAMathematics of the USSR-Izvestiya, 1976
- DISCRETE LINEAR GROUPS GENERATED BY REFLECTIONSMathematics of the USSR-Izvestiya, 1971
- Quasi-homogeneous conesMathematical Notes, 1967
- Discrete Groups Generated by ReflectionsAnnals of Mathematics, 1934