On derived equivalences of lines, rectangles and triangles

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We present a method to construct new tilting complexes from existing ones using tensor products, generalizing a result of Rickard. The endomorphism rings of these complexes are generalized matrix rings that are 'componentwise' tensor products, allowing us to obtain many derived equivalences that have not been observed by using previous techniques.Particular examples include algebras generalizing the ADE-chain related to singularity theory, incidence algebras of posets and certain Auslander algebras or more generally endomorphism algebras of initial preprojective modules over path algebras of quivers. Many of these algebras are fractionally Calabi-Yau and we explicitly compute their CY dimensions. Among the quivers of these algebras, one can find shapes of lines, rectangles and triangles.

Original languageEnglish
Pages (from-to)157-176
Number of pages20
JournalJournal of the London Mathematical Society
Issue number1
StatePublished - Feb 2013
Externally publishedYes

Bibliographical note

Funding Information:
Received 20 September 2011; revised 24 February 2012; published online 14 September 2012. 2010 Mathematics Subject Classification 16E35, 16S50, 16G20, 16G70, 18G15. This work was supported in part by a European Postdoctoral Institute fellowship.

ASJC Scopus subject areas

  • General Mathematics


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