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Picard Groups for Derived Module Categories

Published online by Cambridge University Press:  25 June 2003

Raphaël Rouquier  and
Alexander Zimmermann
Raphaël Rouquier
Affiliation:
UFR de Mathématiques, Université Paris 7 Denis Diderot et UMR 7586 du CNRS, 2 place Jussieu, 75251 Paris Cedex 05, France. E-mail: Raphael.Rouquier@math.jussieu.fr
Alexander Zimmermann
Affiliation:
Faculté de Mathématiques, Université de Picardie Jules Verne et LAMFA UMR 6140 du CNRS, 33 rue Saint Leu, 80039 Amiens Cedex, France. E-mail: Alexander.Zimmermann@u-picardie.fr
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Abstract

In this paper we introduce a generalization of Picard groups to derived categories of algebras. First we study general properties of this group. Then we consider easy particular algebras such as commutative algebras, where we reduce to the classical case. Finally, we define and study a homomorphism of the braid group to the Picard group of the derived category of a Brauer tree algebra. In the smallest case we show that this homomorphism is injective and that its image is of finite index.

Keywords

Picard groupsderived equivalencesBrauer tree algebrasbraid group actions16D9018E3020F36
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 87 , Issue 1 , July 2003 , pp. 197 - 225
Copyright
2003 London Mathematical Society

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