For a radical square zero algebraΛand an indecomposable rightΛ-module M,whenΛis Gorenstein of finite representation type orτM isτ-rigid,M isτ-rigid if and only if the first two projective terms of a minimal proj...For a radical square zero algebraΛand an indecomposable rightΛ-module M,whenΛis Gorenstein of finite representation type orτM isτ-rigid,M isτ-rigid if and only if the first two projective terms of a minimal projective resolution of M have no non-zero direct summands in common.In particular,we determine allτ-tilting modules for Nakayama algebras with radical square zero.展开更多
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 categ...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 T-rigid pairs in the module category of the endomorphism algebra Endc（T）op. As a consequence, basic maximal objects in prT are one-to-one correspondence to basic support τ-tilting modules over Endc（T）op. This is a generalization of correspondences established by Adachi-Iyama-Reiten.展开更多
基金This research is carried out with the support of NSFC(Nos.11571164 and 11671174)NSF of Jiangsu Province(No.BK20130983)NSF for Colleges and Universities in Jiangsu Province of China(No.1 IKJB110007).
文摘For a radical square zero algebraΛand an indecomposable rightΛ-module M,whenΛis Gorenstein of finite representation type orτM isτ-rigid,M isτ-rigid if and only if the first two projective terms of a minimal projective resolution of M have no non-zero direct summands in common.In particular,we determine allτ-tilting modules for Nakayama algebras with radical square zero.
基金supported by National Natural Science Foundation of China(Grant No.11131001)supported by BIT Basic Scientific Research Grant(Grant No.3170012211408)
文摘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 T-rigid pairs in the module category of the endomorphism algebra Endc（T）op. As a consequence, basic maximal objects in prT are one-to-one correspondence to basic support τ-tilting modules over Endc（T）op. This is a generalization of correspondences established by Adachi-Iyama-Reiten.
