Maximal tau-d-rigid pairs

Karin Jacobsen; Peter Jørgensen

doi:10.1016/j.jalgebra.2019.10.046

Maximal tau-d-rigid pairs

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

Let T be a 2-Calabi–Yau triangulated category, T a cluster tilting object with endomorphism algebra Γ. Consider the functor T(T,−):T→modΓ. It induces a bijection from the isomorphism classes of cluster tilting objects to the isomorphism classes of support τ-tilting pairs. This is due to Adachi, Iyama, and Reiten. The notion of (d+2)-angulated categories is a higher analogue of triangulated categories. We show a higher analogue of the above result, based on the notion of maximal τ _d-rigid pairs.

Original language	English
Journal	Journal of Algebra
Volume	546
Pages (from-to)	119-134
Number of pages	16
ISSN	0021-8693
DOIs	https://doi.org/10.1016/j.jalgebra.2019.10.046
Publication status	Published - Mar 2020
Externally published	Yes

Keywords

(d+2)-Angulated category
Higher homological algebra
Maximal d-rigid object
Maximal τ -rigid pair
d-Abelian category

Access to Document

10.1016/j.jalgebra.2019.10.046

Cite this

@article{5d015d91559f4fb096d6182b7b4ded4c,

title = "Maximal tau-d-rigid pairs",

abstract = "Let T be a 2-Calabi–Yau triangulated category, T a cluster tilting object with endomorphism algebra Γ. Consider the functor T(T,−):T→modΓ. It induces a bijection from the isomorphism classes of cluster tilting objects to the isomorphism classes of support τ-tilting pairs. This is due to Adachi, Iyama, and Reiten. The notion of (d+2)-angulated categories is a higher analogue of triangulated categories. We show a higher analogue of the above result, based on the notion of maximal τ d-rigid pairs.",

keywords = "(d+2)-Angulated category, Higher homological algebra, Maximal d-rigid object, Maximal τ -rigid pair, d-Abelian category",

author = "Karin Jacobsen and Peter J{\o}rgensen",

year = "2020",

month = mar,

doi = "10.1016/j.jalgebra.2019.10.046",

language = "English",

volume = "546",

pages = "119--134",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press",

}

TY - JOUR

T1 - Maximal tau-d-rigid pairs

AU - Jacobsen, Karin

AU - Jørgensen, Peter

PY - 2020/3

Y1 - 2020/3

N2 - Let T be a 2-Calabi–Yau triangulated category, T a cluster tilting object with endomorphism algebra Γ. Consider the functor T(T,−):T→modΓ. It induces a bijection from the isomorphism classes of cluster tilting objects to the isomorphism classes of support τ-tilting pairs. This is due to Adachi, Iyama, and Reiten. The notion of (d+2)-angulated categories is a higher analogue of triangulated categories. We show a higher analogue of the above result, based on the notion of maximal τ d-rigid pairs.

AB - Let T be a 2-Calabi–Yau triangulated category, T a cluster tilting object with endomorphism algebra Γ. Consider the functor T(T,−):T→modΓ. It induces a bijection from the isomorphism classes of cluster tilting objects to the isomorphism classes of support τ-tilting pairs. This is due to Adachi, Iyama, and Reiten. The notion of (d+2)-angulated categories is a higher analogue of triangulated categories. We show a higher analogue of the above result, based on the notion of maximal τ d-rigid pairs.

KW - (d+2)-Angulated category

KW - Higher homological algebra

KW - Maximal d-rigid object

KW - Maximal τ -rigid pair

KW - d-Abelian category

UR - http://www.scopus.com/inward/record.url?scp=85074921671&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2019.10.046

DO - 10.1016/j.jalgebra.2019.10.046

M3 - Journal article

SN - 0021-8693

VL - 546

SP - 119

EP - 134

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Maximal tau-d-rigid pairs

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this