A Brief Introduction to the Q-Shaped Derived Category
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A chain complex can be viewed as a representation of a certain quiver with relations, Qcpx. 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 Qcpx. It is an insight of Iyama and Minamoto that the reason D is well behaved is that, viewed as a small category, Qcpx 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, DQ. Drawing on methods of Hovey and Gillespie, we developed the theory of DQ in three recent papers. This paper offers a brief introduction to DQ, aimed at the reader already familiar with the classic derived category.
Original language | English |
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Title of host publication | Triangulated Categories in Representation Theory and Beyond : The Abel Symposium 2022 |
Editors | Petter Andreas Bergh, Øyvind Solberg, Steffen Oppermann |
Number of pages | 27 |
Publisher | Springer |
Publication date | 2024 |
Pages | 141-167 |
ISBN (Print) | 9783031577888 |
DOIs | |
Publication status | Published - 2024 |
Event | Abel Symposium, 2022 - Ålesund, Norway Duration: 6 Jun 2022 → 10 Jun 2022 |
Conference
Conference | Abel Symposium, 2022 |
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Land | Norway |
By | Ålesund |
Periode | 06/06/2022 → 10/06/2022 |
Series | Abel Symposia |
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Volume | 17 |
ISSN | 2193-2808 |
Bibliographical note
Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
- Abelian category, Abelian model category, Chain complex, Cofibration, Derived category, Exact category, Fibration, Frobenius category, Homotopy, Homotopy category, Model category, Stable category, Triangulated category, Weak equivalence
Research areas
ID: 402883585