Abstract
We consider a Krull–Schmidt, Hom-finite, 2-Calabi–Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic τ-rigid pairs in the module category of the endomorphism algebra Endc(T) op . As a consequence, basic maximal objects in pr T are one-to-one correspondence to basic support τ-tilting modules over End c (T) op . This is a generalization of correspondences established by Adachi–Iyama–Reiten.
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The first and third authors are supported by National Natural Science Foundation of China (Grant No. 11131001); the sencond author is supported by BIT Basic Scientific Research Grant (Grant No. 3170012211408)
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Chang, W., Zhang, J. & Zhu, B. On support τ-tilting modules over endomorphism algebras of rigid objects. Acta. Math. Sin.-English Ser. 31, 1508–1516 (2015). https://doi.org/10.1007/s10114-015-4161-4
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DOI: https://doi.org/10.1007/s10114-015-4161-4