caa a22 4500 605461260 CHVBK 20210128100242.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10114-015-4161-4 doi (NATIONALLICENCE)springer-10.1007/s10114-015-4161-4 On support τ -tilting modules over endomorphism algebras of rigid objects [Elektronische Daten] [Wen Chang, Jie Zhang, Bin Zhu] 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. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Rigid object nationallicence maximal rigid object nationallicence τ -rigid object nationallicence finite presented category nationallicence Chang Wen Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P. R. China aut Zhang Jie School of Mathematics and Statistics, Beijing institute of technology, 100081, Beijing, P. R. China aut Zhu Bin Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/9(2015-09-01), 1508-1516 1439-8516 31:9<1508 2015 31 10114 https://doi.org/10.1007/s10114-015-4161-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-4161-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chang Wen Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P. R. China aut NATIONALLICENCE 700 1- Zhang Jie School of Mathematics and Statistics, Beijing institute of technology, 100081, Beijing, P. R. China aut NATIONALLICENCE 700 1- Zhu Bin Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/9(2015-09-01), 1508-1516 1439-8516 31:9<1508 2015 31 10114