Abstract.
We show that the operation of the braid group on the set of complete exceptional sequences in the category of coherent sheaves on an exceptional curve \( \mathbb{X} \) over a field k is transitive. As a consequence the list of endomorphism skew-fields of the indecomposable direct summands of a tilting complex is a derived invariant. Furthermore, we apply the result in order to establish a bijection (which is compatible with the K-theory) between the sets of translation classes of exceptional objects in the derived categories of two derived-canonical algebras with the same Cartan matrix, but which are defined over possibly distinct fields.
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Eingegangen am 25. 9. 2000
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ID="h1"Dedicated to Professor Idun Reiten on the occasion of her 60th birthday
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Kussin, D., Meltzer, H. The braid group action for exceptional curves. Arch. Math. 79, 335–344 (2002). https://doi.org/10.1007/PL00012455
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DOI: https://doi.org/10.1007/PL00012455