22
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Ptolemy diagrams and torsion pairs in m-cluster categories of type D

Pages 4499-4514 | Received 28 Sep 2022, Accepted 19 Apr 2024, Published online: 14 May 2024

References

  • Beǐlinson, A. A., Bernstein, J., Deligne, P. (1982). Faisceaux pervers. Analysis and topology on singular spaces, I (Luminy, 1981), Astérisque, 100. Paris: Société Mathématique de France, pp. 5–171.
  • Baur, K., Marsh, R. (2008). A geometric description of m-cluster categories. Trans. Amer. Math. Soc. 360:5789–5803.
  • Baur, K., Marsh, R. (2007). A geometric description of m-cluster categories of type Dn. Int. Math. Res. Not. 2007:rnm011. DOI: 10.1093/imrn/rnm011.
  • Buan, A. B., Marsh, R., Reineke, M., Reiten, I., Todorov, G. (2006). Tilting theory and cluster combinatorics. Adv. Math. 204(2):572–618.
  • Caldero, P., Chapoton, F., Schiffler, R. (2006). Quivers with relations arising from clusters (An case). Trans. Amer. Math. Soc. 358(3):1347–1364.
  • Chang, H., Zhou, Y., Zhu, B. (2018). Cotorsion pairs in cluster categories of type A∞∞. J. Combin. Theory Ser. A 156:119–141.
  • Chang, H., Zhu, B. (2019). Torsion pairs in finite 2-Calabi-Yau triangulated categories with maximal rigid objects. Commun. Algebra 47(7):2810–2832.
  • Chang, H., Zhu, B. (2023). Cotorsion pairs in m-cluster categories of type A. J. Algebra Appl. 22(12):2350248.
  • Fomin, S., Zelevinsky, A. (2003). Y-systems and generalized associahedra. Ann. Math. 158:977–1018.
  • Gratz, S., Holm, T., Jørgensen, P. (2019). Cluster tilting subcategories and torsion pairs in Igusa-Todorov cluster categories of Dynkin type A∞. Math. Z. 292:33–56.
  • Holm, T., Jørgensen, P. (2012). On a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon. Math. Z. 270:277–295.
  • Holm, T., Jørgensen, P., Rubey, M. (2011). Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type An. J. Algebraic Combin. 34(3):507–523.
  • Holm, T., Jørgensen, P., Rubey, M. (2014). Torsion pairs in cluster tubes. J. Algebraic Combin. 39(3):587–605.
  • Holm, T., Jørgensen, P., Rubey, M. (2013). Ptolemy diagrams and torsion pairs in the cluster categories of Dynkin type D. Adv. Appl. Math. 51(5):583–605.
  • Iyama, O., Yoshino, Y. (2008). Mutation in triangulated categories and rigid Cohen-Macaulay modules. Invent. Math. 172(1):117–168.
  • Jacquet-Malo, L. (2022). A bijection between m-cluster tilting objects and (m+2)-angulations in m-cluster categories. J. Algebra 595:581–632.
  • Keller, B. (2005). On triangulated orbit categories. Doc. Math. 10:551–581.
  • Keller, B., Reiten, I. (2007). Cluster-tilted algebras are Gorenstein and stably Calabi-Yau. Adv. Math. 211(1):123–151.
  • Koenig, S., Zhu, B. (2008). From triangulated categories to abelian categories: cluster tilting in a general framework. Math. Z. 258(1):143–160.
  • Nakaoka, H. (2001). General heart construction on a triangulated category (I): Unifying t-structures and cluster tilting subcategories. Appl. Categ. Struct. 19(6):879–899.
  • Ng, P. A characterization of torsion theories in the cluster category of type A∞. arXiv:1005.4364.
  • Schiffler, R. (2008). A geometric model for cluster categories of type Dn. J. Algebraic Combin. 27:1–21.
  • Thomas, H. (2007). Defining an m-cluster category. J. Algebra 318:37–46.
  • Thomas, H. Defining an m-cluster category. arXiv: 0607173v1.
  • Zhang, J., Zhou, Y., Zhu, B. (2013). Cotorsion pairs in the cluster category of a marked surface. J. Algebra 391:209–226.
  • Zhou, Y., Zhu, B. (2009). Cluster combinatorics of d-cluster categories. J. Algebra 321:2898–2915.
  • Zhou, Y., Zhu, B. (2014). T-structures and torsion pairs in a 2-Calabi-Yau triangulated category. J. London Math. Soc. (2) 89(1):213–234.
  • Zhu, B. (2008). Generalized cluster complexes via quiver representations. J. Algebraic Combin. 27:25–54.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.