Geodesic
On triangulated orbit categories
Documenta mathematica, Tome 10 (2005), pp. 551-581.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We show that the category of orbits of the bounded derived category of a hereditary category under a well-behaved autoequivalence is canonically triangulated. This answers a question by Aslak Buan, Robert Marsh and Idun Reiten which appeared in their study citeBuanMarshReinekeReitenTodorov04 with M. Reineke and G. Todorov of the link between tilting theory and cluster algebras ($\cf $also citeCalderoChapotonSchiffler04) and a question by Hideto Asashiba about orbit categories. We observe that the resulting triangulated orbit categories provide many examples of triangulated categories with the Calabi-Yau property. These include the category of projective modules over a preprojective algebra of generalized Dynkin type in the sense of Happel-Preiser-Ringel citeHappelPreiserRingel80, whose triangulated structure goes back to Auslander-Reiten's work citeAuslanderReiten87, citeReiten87, citeAuslanderReiten96.
Classification : 18E30, 16G20
Keywords: derived category, triangulated category, orbit category, Calabi-Yau category 
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     author = {Keller, Bernhard},
     title = {On triangulated orbit categories},
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Keller, Bernhard. On triangulated orbit categories. Documenta mathematica, Tome 10 (2005), pp. 551-581. http://geodesic.mathdoc.fr/item/DOCMA_2005__10__a2/