Automorphisms of Green Orders and Their Derived Categories |
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Authors: | Alexander Zimmermann |
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Affiliation: | (1) Faculté de Mathématiques, LAMFA (UMR 6140 du CNRS), Université de Picardie 33, rue St Leu, 80039 Amiens Cedex, France |
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Abstract: | In an earlier paper, Raphaël 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 nontrivial homomorphism of the Artin braid group to this group of self-equivalences. The class of Brauer tree algebras include 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. |
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Keywords: | derived categories Green orders Brauer tree algebra |
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