Fetching the paper…
Reading the bibliography…
We study the cluster category of a canonical algebra A in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line X.
J.-L. Verdier, Catégories dérivées (etat 0). (french) in: P. Deligne ed.: Séminarie de Géométrie Algébrique du Bois-Marie SGA 4 1 2 \frac{1}{2} . Lecture Notes in Mathematics 569
1977
Earlier work this paper cites.
M. Auslander, M. I. Platzeck and I. Reiten: Coxeter functors without diagrams
1979
Earlier work this paper cites.
C. M. Ringel, Tame algebras and integral quadratic forms. Lecture Notes in Mathematics 1099
1984
Earlier work this paper cites.
W. Geigle and H. Lenzing, A class of weighted projective curves arising in representation theory of finite-dimensional algebras. Springer Lecture Notes in Math. 1273
1987
Earlier work this paper cites.
D. Happel, Triangulated Categories in the Representation Theory of Finite Dimensional Algebras. Cambridge University Press, Cambridge, 1988
1988
Earlier work this paper cites.
by same author, The canonical algebras. Topics in Algebra, Part I. Banach Center Publ., no. 26, PWN, 1990, With an appendix by William Crawley-Boevey, pp. 407–432
1990
Earlier work this paper cites.
by same author, Perpendicular categories with applications to representations and sheaves
1991
Earlier work this paper cites.
J. Rickard, Derived equivalences as derived functors. J. London Math. Soc. 43
1991
Earlier work this paper cites.
H. Lenzing and H. Meltzer, Sheaves on a weighted projective line of genus one, and representations of a tubular algebra. CMS Conf. Proc. 14
1992
Earlier work this paper cites.
by same author, Tilting sheaves and concealed-canonical algebras. CMS Conf. Proc. 14
1992
Cited alongside, same era.
T. Hübner, Exzeptionelle Vektorbündel und Reflektionen an Kippgarben über projektiven gewichteten Kurven. Dissertation, Universität Paderborn, 1996
1996
Cited alongside, same era.
by same author, Rank additivity for quasi-tilted algebras of canonical type . Colloq. Math. 75
1998
Cited alongside, same era.
H. Lenzing, Representations of finite dimensional algebras and singularity theory , Trends in ring theory (Miskolc, 1996) (V. Dlab et al., ed.), CMS Conf. Proc., vol. 22, Amer. Math. Soc., Providence, RI, 1998, pp. 71–97
1998
Cited alongside, same era.
H. Lenzing and J.A. de la Peña, Concealed-canonical algebras and separating tubular families. Proc. London Math. Soc. (3) 78
1999
Cited alongside, same era.
D. Happel and L. Unger, On the set of tilting objects in hereditary categories. Fields Institute Communications 45 (2005), 141–159
2005
Later among the works it cites.
B. Keller, On triangulated orbit categories. Documenta Math. 10
2005
Later among the works it cites.
A. Buan, R. Marsh, M. Reineke, I. Reiten and G. Todorov, Tilting theory and cluster combinatorics . Adv. Math. 204
2006
Later among the works it cites.
B. Zhu, Equivalences between cluster categories. J. Algebra 304
2006
Later among the works it cites.
A. Buan, O. Iyama, I. Reiten and J. Scott, Cluster structures for 2-Calabi-Yau categories and unipotent groups. Preprint (2007) arXiv:math/0701557
2007
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
H. Lenzing and I. Reiten, Additive functions for quivers with relations . Colloq. Math. 82
1999
Cited alongside, same era.
by same author, The automorphism group of the derived category for a weighted projective line. Comm. Algebra 28
2000
Cited alongside, same era.
S. Fomin, A. Zelevinsky, Cluster algebras I: Foundations . J. Amer. Math. Soc. 15
2002
Cited alongside, same era.
H. Meltzer, Exceptional vector bundles, tilting sheaves and tilting complexes for weighted projective lines. Mem. Amer. Math. Soc. 171
2004
Cited alongside, same era.
D. Kussin, Noncommutative curves of genus zero – related to finite dimensional algebras. Mem. Amer. Math. Soc., to appear
Cited in the paper.
M. Barot, D. Kussin and H. Lenzing, The Grothendieck group of a cluster category. J. Pure Appl. Algebra 212
2008
Closest in time.
O. Iyama and Y. Yoshino, Mutation in triangulated categories and rigid Cohen-Macaulay modules. Invent. Math. 172
2008
Closest in time.
by same author, Parameter curves for the regular representations of tame bimodules. J. Algebra 320
2008
Closest in time.