On support τ-tilting modules over endomorphism algebras of rigid objects

Wen Chang; Jie Zhang; Bin Zhu

doi:10.1007/s10114-015-4161-4

On support τ-tilting modules over endomorphism algebras of rigid objects

Wen Chang, Jie Zhang^*, Bin Zhu

^*Corresponding author for this work

School of Mathematics and Statistics

Tsinghua University

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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 End_c(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.

Original language	English
Pages (from-to)	1508-1516
Number of pages	9
Journal	Acta Mathematica Sinica, English Series
Volume	31
Issue number	9
DOIs	https://doi.org/10.1007/s10114-015-4161-4
Publication status	Published - 8 Sept 2015

Keywords

Rigid object
finite presented category
maximal rigid object
τ-rigid object

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10.1007/s10114-015-4161-4

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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 Endc(T)op. This is a generalization of correspondences established by Adachi–Iyama–Reiten.",

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AU - Chang, Wen

AU - Zhang, Jie

AU - Zhu, Bin

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N2 - 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 Endc(T)op. This is a generalization of correspondences established by Adachi–Iyama–Reiten.

AB - 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 Endc(T)op. This is a generalization of correspondences established by Adachi–Iyama–Reiten.

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KW - finite presented category

KW - maximal rigid object

KW - τ-rigid object

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On support τ-tilting modules over endomorphism algebras of rigid objects

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Keywords

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