A Brief Introduction to the Q-Shaped Derived Category

Henrik Holm; Peter Jørgensen

doi:10.1007/978-3-031-57789-5_5

A Brief Introduction to the Q-Shaped Derived Category

Henrik Holm, Peter Jørgensen^*

^*Corresponding author af dette arbejde

Institut for Matematiske Fag

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

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Abstract

A chain complex can be viewed as a representation of a certain quiver with relations, Q^cpx. The vertices are the integers, there is an arrow q right arrow Overscript Endscripts q minus 1) for each integer q, and the relations are that consecutive arrows compose to 0. Hence the classic derived category D can be viewed as a category of representations of Q^cpx. It is an insight of Iyama and Minamoto that the reason D is well behaved is that, viewed as a small category, Q^cpx has a Serre functor. Generalising the construction of D to other quivers with relations which have a Serre functor results in the Q-shaped derived category, D_Q. Drawing on methods of Hovey and Gillespie, we developed the theory of D_Q in three recent papers. This paper offers a brief introduction to D_Q, aimed at the reader already familiar with the classic derived category.

Originalsprog	Engelsk
Titel	Triangulated Categories in Representation Theory and Beyond : The Abel Symposium 2022
Redaktører	Petter Andreas Bergh, Øyvind Solberg, Steffen Oppermann
Antal sider	27
Forlag	Springer
Publikationsdato	2024
Sider	141-167
ISBN (Trykt)	9783031577888
DOI	https://doi.org/10.1007/978-3-031-57789-5_5
Status	Udgivet - 2024
Begivenhed	Abel Symposium, 2022 - Ålesund, Norge Varighed: 6 jun. 2022 → 10 jun. 2022

Konference

Konference	Abel Symposium, 2022
Land/Område	Norge
By	Ålesund
Periode	06/06/2022 → 10/06/2022

Navn	Abel Symposia
Vol/bind	17
ISSN	2193-2808

Bibliografisk note

Funding Information:
The scientific and organising committee of the Abel Symposium 2022 consisted of Paul Balmer, Petter Andreas Bergh, Bernhard Keller, Henning Krause, Steffen Oppermann, and \u00D8yvind Solberg. We thank them for the invitation to give a talk on this material and to submit this paper to the proceedings of the symposium. Part of this paper was written when the second author was a Fellow at the Centre for Advanced Study of the Norwegian Academy of Science and Letters. He thanks the Centre for its hospitality and the organisers, Aslak Buan and Steffen Oppermann, for the invitation to attend the programme \u201CRepresentation Theory: Combinatorial Aspects and Applications\u201D. This work was supported by a DNRF Chair from the Danish National Research Foundation (grant DNRF156), by a Research Project 2 from the Independent Research Fund Denmark (grant 1026-00050B), and by Aarhus University Research Foundation (grant AUFF-F-2020-7-16).

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Adgang til dokumentet

10.1007/978-3-031-57789-5_5

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Citationsformater

A Brief Introduction to the Q-Shaped Derived Category. / Holm, Henrik; Jørgensen, Peter.

Triangulated Categories in Representation Theory and Beyond: The Abel Symposium 2022. red. / Petter Andreas Bergh; Øyvind Solberg; Steffen Oppermann. Springer, 2024. s. 141-167 (Abel Symposia, Bind 17).

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

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KW - Fibration

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