2,037 research outputs found
Hochschild cohomology and derived Picard groups
We interpret Hochschild cohomology as the Lie algebra of the derived Picard
group (in the sense of Rouquier-Zimmermann and Yekutieli) and deduce that it is
preserved under derived equivalences.Comment: 15 pages, accepted for publication in JPA
Cluster algebras, quiver representations and triangulated categories
This is an introduction to some aspects of Fomin-Zelevinsky's cluster
algebras and their links with the representation theory of quivers and with
Calabi-Yau triangulated categories. It is based on lectures given by the author
at summer schools held in 2006 (Bavaria) and 2008 (Jerusalem). In addition to
by now classical material, we present the outline of a proof of the periodicity
conjecture for pairs of Dynkin diagrams (details will appear elsewhere) and
recent results on the interpretation of mutations as derived equivalences.Comment: 53 pages, references update
On differential graded categories
Differential graded categories enhance our understanding of triangulated
categories appearing in algebra and geometry. In this survey, we review their
foundations and report on recent work by Drinfeld, Dugger-Shipley, ..., Toen
and Toen-Vaquie.Comment: 30 pages, correction at the end of 3.9, corrections and added
references in 5.
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