Maximal tau-d-rigid pairs

Karin Jacobsen; Peter Jørgensen

doi:10.1016/j.jalgebra.2019.10.046

Maximal tau-d-rigid pairs

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

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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.

Originalsprog	Engelsk
Tidsskrift	Journal of Algebra
Vol/bind	546
Sider (fra-til)	119-134
Antal sider	16
ISSN	0021-8693
DOI	https://doi.org/10.1016/j.jalgebra.2019.10.046
Status	Udgivet - 15 mar. 2020
Udgivet eksternt	Ja

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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,

day = "15",

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

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journal = "Journal of Algebra",

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T1 - Maximal tau-d-rigid pairs

AU - Jacobsen, Karin

AU - Jørgensen, Peter

PY - 2020/3/15

Y1 - 2020/3/15

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 - https://www.scopus.com/pages/publications/85074921671

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

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