A construction of derived equivalent pairs of symmetric algebras

Details A construction of derived equivalent pairs of symmetric algebras A construction of derived equivalent pairs of symmetric algebras

2010-05-27

arxiv.org/abs/1005.5152v3

Mathematics

Representation Theory

Added Lemma 3.4 to clear up a step in the proof of the main theorem

Scientific paper

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 more general class of triangles (in algebraic triangulated categories) for which the endomorphism rings of different terms are derived equivalent. In particular, applying this result in the category of perfect complexes over a symmetric algebra gives a new 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.

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