Automorphisms of Green orders and their derived categories
Alexander Zimmermann
October 2000; revised May 2001

Abstract. In an earlier paper Rapha\"el Rouquier and the author introduced
the group of self-equivalences of a derived category. In the case of a Brauer
tree algebra we determined a non trivial homomorphism of the Artin braid group
to this group of self-equivalences. The class of Brauer tree algebras includes
blocks of finite group rings over a large enough field with cyclic defect
groups. In the present paper we give an integral version of this homomorphism.
Moreover, we identify some interesting arithmetic subgroups with natural groups
of self-equivalences of the derived category.