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Ladders of Compactly Generated Triangulated Categories and Preprojective Algebras

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Abstract

In this paper we characterize when a recollement of compactly generated triangulated categories admits a ladder of some height going either upwards or downwards. As an application, we show that the derived category of the preprojective algebra of Dynkin type \(\mathbb {A}_n\) admits a periodic infinite ladder, where the one outer term in the recollement is the derived category of a differential graded algebra.

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Acknowledgements

The authors would like to thank Steffen Koenig, Julian Külshammer, Frederik Marks and Jorge Vitória for useful discussions and valuable comments. The authors wish to thank the referee for the useful suggestions and remarks.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Nan Gao

  2. Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Chrysostomos Psaroudakis

Authors
  1. Nan Gao
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  2. Chrysostomos Psaroudakis
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Correspondence to Chrysostomos Psaroudakis.

Additional information

Communicated by Henning Krause.

Nan Gao is supported by Natural Science foundation of China (11771272).

Chrysostomos Psaroudakis was supported by the Norwegian Research Council (NFR 221893) under the project Triangulated categories in Algebra at the Norwegian University of Science and Technology (NTNU).

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Gao, N., Psaroudakis, C. Ladders of Compactly Generated Triangulated Categories and Preprojective Algebras. Appl Categor Struct 26, 657–679 (2018). https://doi.org/10.1007/s10485-017-9508-9

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  • DOI: https://doi.org/10.1007/s10485-017-9508-9

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