Derived autoequivalences from periodic algebras

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We present a construction of autoequivalences of derived categories of symmetric algebras based on projective modules with periodic endomorphism algebras. This construction generalizes autoequivalences previously constructed by Rouquier–Zimmermann and is related to the autoequivalences of Seidel–Thomas and Huybrechts–Thomas. We show that compositions and inverses of these equivalences are controlled by the resolutions of our endomorphism algebra and that each autoequivalence can be obtained by certain compositions of derived equivalences between algebras which are in general not Morita equivalent.
Original languageEnglish
Pages (from-to)375-409
Number of pages35
JournalProceedings of the London Mathematical Society
Issue number2
Early online date30 Aug 2012
Publication statusPublished - Feb 2013

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