  Using the classification of finite Weyl groupoids we prove that
crystallographic arrangements, a large subclass of the class of simplicial
arrangements which was recently defined, are hereditarily inductively free. In
particular, all crystallographic reflection arrangements are hereditarily
inductively free, among them the arrangement of type $E_8$. With little extra
work we prove that also all Coxeter arrangements are inductively free.

Combinatorics;Quantum Algebra