Representations of thread quivers

Carl Fredrik Berg; Adam Christiaan Van Roosmalen

doi:10.1112/plms/pdt021

Representations of thread quivers

Carl Fredrik Berg, Adam Christiaan Van Roosmalen

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

4 Citations (Scopus)

Abstract

We introduce thread quivers as an (infinite) generalization of quivers, and show that every k-linear (k algebraically closed) hereditary category with Serre duality and enough projectives is equivalent to the category of finitely presented representations of a thread quiver. In this way, we obtain an explicit construction of a new class of hereditary categories with Serre duality.

Original language	English
Pages (from-to)	253-290
Number of pages	38
Journal	Proceedings of the London Mathematical Society
Volume	108
Issue number	2
DOIs	https://doi.org/10.1112/plms/pdt021
Publication status	Published - Feb 2014
Externally published	Yes

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Berg, C. F., & Van Roosmalen, A. C. (2014). Representations of thread quivers. Proceedings of the London Mathematical Society, 108(2), 253-290. https://doi.org/10.1112/plms/pdt021

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abstract = "We introduce thread quivers as an (infinite) generalization of quivers, and show that every k-linear (k algebraically closed) hereditary category with Serre duality and enough projectives is equivalent to the category of finitely presented representations of a thread quiver. In this way, we obtain an explicit construction of a new class of hereditary categories with Serre duality.",

author = "Berg, {Carl Fredrik} and {Van Roosmalen}, {Adam Christiaan}",

note = "Funding Information: Acknowledgements. The authors would like to thank Idun Reiten, Sverre Smal{\o}, and Michel Van den Bergh for their many useful discussions and helpful ideas. We would also like to thank Tobias Fritz for pointing us to [28], and Catharina Stroppel for her useful comments on an earlier version of this article. The second author gratefully acknowledges the hospitality and support of the Max-Planck-Institut f{\"u}r Mathematik in Bonn, the Norwegian University of Science and Technology, and the University of Regina.",

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N1 - Funding Information: Acknowledgements. The authors would like to thank Idun Reiten, Sverre Smalø, and Michel Van den Bergh for their many useful discussions and helpful ideas. We would also like to thank Tobias Fritz for pointing us to [28], and Catharina Stroppel for her useful comments on an earlier version of this article. The second author gratefully acknowledges the hospitality and support of the Max-Planck-Institut für Mathematik in Bonn, the Norwegian University of Science and Technology, and the University of Regina.

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Y1 - 2014/2

N2 - We introduce thread quivers as an (infinite) generalization of quivers, and show that every k-linear (k algebraically closed) hereditary category with Serre duality and enough projectives is equivalent to the category of finitely presented representations of a thread quiver. In this way, we obtain an explicit construction of a new class of hereditary categories with Serre duality.

AB - We introduce thread quivers as an (infinite) generalization of quivers, and show that every k-linear (k algebraically closed) hereditary category with Serre duality and enough projectives is equivalent to the category of finitely presented representations of a thread quiver. In this way, we obtain an explicit construction of a new class of hereditary categories with Serre duality.

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JF - Proceedings of the London Mathematical Society

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Representations of thread quivers

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