Derived autoequivalences from periodic algebras

Abstract

We present a construction of autoequivalences of derived categories of symmetric algebras based on projective modules with periodic endomorphism algebras. This construction generalises 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.

34 pages; v2 is post referee report. The biggest changes from v1 are in Section 5.2. Final version has appeared in Proc. LMS

References in corpus (2)

• Degenerations for derived categories
• Homotopy types of truncated projective resolutions

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• Higher zigzag algebras