A construction of derived equivalent pairs of symmetric algebras

Abstract

Recently, Hu and Xi have exhibited derived equivalent endomorphism rings arising from (relative) almost split sequences as well as AR-triangles in triangulated categories. We present a broader class of triangles (in algebraic triangulated categories) for which the endomorphism rings of different terms are derived equivalent. We then study applications involving 0-Calabi-Yau triangulated categories. In particular, applying our results in the category of perfect complexes over a symmetric algebra gives a nice way of producing pairs of derived equivalent symmetric algebras. Included in the examples we work out are some of the algebras of dihedral type with two or three simple modules. We also apply our results to stable categories of Cohen-Macaulay modules over odd-dimensional Gorenstein hypersurfaces having an isolated singularity.