Combinatorial derived invariants for gentle algebras

Details Combinatorial derived invariants for gentle algebras Combinatorial derived invariants for gentle algebras

2006-07-14

arxiv.org/abs/math/0607348v3

Mathematics

Representation Theory

22 pages, slightly reorganized and an example added, final version. To appear in J. Pure Appl. Algebra

Scientific paper

10.1016/j.jpaa.2007.05.014

We define derived equivalent invariants for gentle algebras, constructed in an easy combinatorial way from the quiver with relations defining these algebras. Our invariants consist of pairs of natural numbers and contain important information about the algebra and the structure of the stable Auslander-Reiten quiver of its repetitive algebra. As a by-product we obtain that the number of arrows of the quiver of a gentle algebra is invariant under derived equivalence. Finally, our invariants separate the derived equivalence classes of gentle algebras with at most one cycle.

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