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brauer tree algebras

Proceedings of the London Mathematical Society (1)

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Picard Groups for Derived Module Categories
Raphaël Rouquier, Alexander Zimmermann
Journal:

Proceedings of the London Mathematical Society / Volume 87 / Issue 1 / July 2003

Published online by Cambridge University Press:

25 June 2003, pp. 197-225

Print publication:

July 2003
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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.