Dynkin Diagrams and Root Systems of Indefinite Quasi-Hyperbolic Kac-Moody Algebra QHA₄⁽²⁾

Root Systems and Dynkin Diagrams

In 1969, Murray Gell-Mann won the nobel prize in physics “for his contributions and discoveries concerning the classification of elementary particles and their interactions.” He is the scientist who first used the word quark, and he was the first to describe the SU3(C) flavor symmetry of the hadrons. By organizing the particles according to the root system of the lie algebra su3(C) associated t...

Hyperbolic Kac–moody Superalgebras

We present a classification of the hyperbolic Kac–Moody (HKM) superalgebras. The HKM superalgebras of rank r ≥ 3 are finite in number (213) and limited in rank (6). The Dynkin–Kac diagrams and the corresponding simple root systems are determined. We also discuss a class of singular sub(super)algebras obtained by a folding procedure. MSC number: 17B65, 17B67 LAPTH-1068/04 DSF-TH-28/04 math-ph/04...

Automorphic correction of the hyperbolic Kac-Moody algebra E10

On Root Multiplicities of Some Hyperbolic Kac-Moody Algebras

Using the coset construction, we compute the root multiplicities at level three for some hyperbolic Kac-Moody algebras including the basic hyperbolic extension of A (1) 1 and E10. Member of the CNRS Laboratoire de la Direction des Sciences de la Matière du Commisariat à l’Energie Atomique.

Generalized Dynkin Diagrams and Root Systems and Their Folding Generalized Dynkin Diagrams and Root Systems and Their Folding

Graphs which generalize the simple or aane Dynkin diagrams are introduced. Each diagram deenes a bilinear form on a root system and thus a reeection group. We present some properties of these groups and of their natural \Coxeter element". The folding of these graphs and groups is also discussed, using the theory of C-algebras. Abstract Graphs which generalize the simple or aane Dynkin diagrams ...