Premium
Picard Groups for Derived Module Categories
Author(s) -
Rouquier Raphaël,
Zimmermann Alexander
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611503014059
Subject(s) - mathematics , homomorphism , injective function , picard group , generalization , pure mathematics , braid group , group (periodic table) , commutative property , algebra homomorphism , algebra over a field , discrete mathematics , mathematical analysis , chemistry , organic chemistry
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. 2000 Mathamatics Subject Classification 16D90, 18E30, 20F36