References
- Auslander, M. (1984). Relations for Grothendieck groups of Artin algebras. Proc. Am. Math. Soc. 91(3):336–340. DOI: 10.1090/S0002-9939-1984-0744624-1.
- Butler, M. C. R. (1981). Grothendieck Groups and Almost Split Sequences, Integral Representations and Applications. Berlin; Heidelberg: Springer.
- Barot, M., Kussin, D., Lenzing, H. (2008). The Grothendieck group of a cluster category. J. Pure. Appl. Algebra 212:33–46. DOI: 10.1016/j.jpaa.2007.04.007.
- Baur, K., Marsh, R. (2008). A geometric description of m-cluster categories. Trans. Amer. Math. Soc. 360:5789–5803. DOI: 10.1090/S0002-9947-08-04441-3.
- Baur, K., Marsh, R. (2007). A geometric description of m-cluster categories of type Dn. Int. Math. Res. Not. DOI: 10.1093/imrn/rnm011.
- Buan, A. B., Marsh, R. (2013). From triangulated categories to module categories via localization. Trans. Amer. Math. Soc. 365(6):2845–2861. DOI: 10.1090/S0002-9947-2012-05631-5.
- Buan, A. B., Marsh, R., Reineke, M., Reiten, I., Todorov, G. (2006). Tilting theory and cluster combinatorics. Adv. Math. 204(2):572–618. DOI: 10.1016/j.aim.2005.06.003.
- Caldero, P., Chapoton, F., Schiffler, R. (2006). Quivers with relations arising from clusters (An case). Trans. Am. Math. Soc. 358(3):1347–1364. DOI: 10.1090/S0002-9947-05-03753-0.
- Chang, H. Ptolemy diagrams and torsion pairs in m-cluster categories of type D. arXiv:2312.02526.
- Fedele, F. (2020). Grothendieck groups of triangulated categories via cluster tilting subcategories. Nagoya Math. J. 244:204–231. DOI: 10.1017/nmj.2020.12.
- Fomin, S., Zelevinsky, A. (2003). Y-systems and generalized associahedra. Ann. Math. 158:977–1018. DOI: 10.4007/annals.2003.158.977.
- 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. DOI: 10.1016/j.aam.2013.07.005.
- Iyama, O., Yoshino, Y. (2008). Mutation in triangulated categories and rigid Cohen-Macaulay modules. Invent. Math. 172(1):117–168. DOI: 10.1007/s00222-007-0096-4.
- 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. DOI: 10.4171/dm/199.
- Keller, B., Reiten, I. (2007). Cluster-tilted algebras are Gorenstein and stably Calabi-Yau. Adv. Math. 211(1):123–151. DOI: 10.1016/j.aim.2006.07.013.
- Thomas, H. (2007). Defining an m-cluster category. J. Algebra 318:37–46.
- Xiao, J., Zhu, B. (2002). Relations for the Grothendieck groups of triangulated categories. J. Algebra 257:37–50. DOI: 10.1016/S0021-8693(02)00122-9.
- Zhou, Y., Zhu, B. (2009). Cluster combinatorics of d-cluster categories. J. Algebra 321:2898–2915. DOI: 10.1016/j.jalgebra.2009.01.032.
- Zhu, B. (2008). Generalized cluster complexes via quiver representations. J. Algebraic Combin. 27:25–54.
- Zhu, B., Zhuang, X. (2021). Grothendieck groups in extriangulated categories. J. Algebra 574:206–232. DOI: 10.1016/j.jalgebra.2021.01.029.