We construct (0,2)-graphs from root systems with simply laced diagram and study their properties.

1 Faculty of Biology, Institute of Biology II/Botany, Albert-Ludwigs-University of Freiburg, Freiburg, Germany, 2 Centre of Biological Systems Analysis, Albert-LudwigsUniversity of Freiburg, Freiburg, Germany, 3 Freiburg Institute of Advanced Sciences (FRIAS), Albert-Ludwigs-University of Freiburg, Freiburg, Germany and 4 Centre for Biological Signalling Studies (BIOSS), Albert-Ludwigs-Universi...

Arithmetic root systems are invariants of Nichols algebras of diagonal type with a certain finiteness property. They can also be considered as generalizations of ordinary root systems with rich structure and many new examples. On the other hand, Nichols algebras are fundamental objects in the construction of quantized enveloping algebras, in the noncommutative differential geometry of quantum g...

This is a brief review of root systems and Coxeter groups, intended as background material for a course on double affine Hecke algebras and Macdonald polynomials. They are still incomplete in places. 1. Root systems Much of this material can be found in [Bou]. Let V be a real vector space with a positive definite inner product 〈·, ·〉. If α ∈ V is a non-zero vector, define the reflection sα in t...