From triangulated categories to cluster algebras II

Caldero, Philippe; Keller, Bernhard

doi:10.1016/j.ansens.2006.09.003

Caldero, Philippe ¹ ; Keller, Bernhard

¹ Université Claude Bernard Lyon I, Département de mathématiques, 69622 Villeurbanne Cedex (France)

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 6, pp. 983-1009.

MR Zbl | 2 citations dans Numdam

DOI : 10.1016/j.ansens.2006.09.003

Affiliations des auteurs :

Caldero, Philippe ¹ ; Keller, Bernhard

¹ Université Claude Bernard Lyon I, Département de mathématiques, 69622 Villeurbanne Cedex (France)

@article{ASENS_2006_4_39_6_983_0,
     author = {Caldero, Philippe and Keller, Bernhard},
     title = {From triangulated categories to cluster algebras {II}},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {983--1009},
     publisher = {Elsevier},
     volume = {Ser. 4, 39},
     number = {6},
     year = {2006},
     doi = {10.1016/j.ansens.2006.09.003},
     mrnumber = {2316979},
     zbl = {05149415},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.ansens.2006.09.003/}
}

TY  - JOUR
AU  - Caldero, Philippe
AU  - Keller, Bernhard
TI  - From triangulated categories to cluster algebras II
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2006
SP  - 983
EP  - 1009
VL  - 39
IS  - 6
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.ansens.2006.09.003/
DO  - 10.1016/j.ansens.2006.09.003
LA  - en
ID  - ASENS_2006_4_39_6_983_0
ER  -

%0 Journal Article
%A Caldero, Philippe
%A Keller, Bernhard
%T From triangulated categories to cluster algebras II
%J Annales scientifiques de l'École Normale Supérieure
%D 2006
%P 983-1009
%V 39
%N 6
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.ansens.2006.09.003/
%R 10.1016/j.ansens.2006.09.003
%G en
%F ASENS_2006_4_39_6_983_0

Caldero, Philippe; Keller, Bernhard. From triangulated categories to cluster algebras II. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 6, pp. 983-1009. doi : 10.1016/j.ansens.2006.09.003. http://archive.numdam.org/articles/10.1016/j.ansens.2006.09.003/

Bibliographie
Cité par

[1] Bondal A.I., Kapranov M.M., Representable functors, Serre functors, and reconstructions, Izv. Akad. Nauk SSSR Ser. Mat. 53 (6) (1989) 1183-1205, 1337. | MR | Zbl

[2] Brenner S., Butler M.C.R., The equivalence of certain functors occurring in the representation theory of Artin algebras and species, J. LMS 14 (1) (1976) 183-187. | MR | Zbl

[3] Buan A.B., Marsh R.J., Reiten I., Cluster tilted algebras, Trans. Amer. Math. Soc. 359 (2007) 323-332. | MR | Zbl

[4] Buan A.B., Marsh R.J., Reiten I., Cluster mutation via quiver representations, Comment. Math. Helv., submitted for publication, math.RT/0412077.

[5] Buan A.B., Marsh R.J., Reiten I., Todorov G., Clusters and seeds in acyclic cluster algebras. Appendix by A.B. Buan, R.J. Marsh, P. Caldero, B. Keller, I. Reiten, and G. Todorov, Proc. Amer. Math. Soc., submitted for publication, math.RT/0510359.

[6] Buan A.B., Marsh R.J., Reineke M., Reiten I., Todorov G., Tilting theory and cluster combinatorics, Adv. Math., submitted for publication, math.RT/0402054. | MR | Zbl

[7] Caldero P., Chapoton F., Cluster algebras as Hall algebras of quiver representations, Comment. Math. Helv. 81 (2006) 595-616, math.RT/0410184. | MR | Zbl

[8] Caldero P., Chapoton F., Schiffler R., Quivers with relations arising from clusters ( $A_{n}$ case), Trans. Amer. Math. Soc. 358 (2006) 1347-1364. | MR | Zbl

[9] Caldero P., Chapoton F., Schiffler R., Quivers with relations and cluster tilted algebras, J. Alg. and Rep. Th., submitted for publication, math.RT/0411238. | MR | Zbl

[10] Caldero P., Keller B., From triangulated categories to cluster algebras, Invent. Math., submitted for publication, math.RT/0506018. | Zbl

[11] Fomin S., Zelevinsky A., Cluster algebras. I. Foundations, J. Amer. Math. Soc. 15 (2) (2002) 497-529. | MR | Zbl

[12] Fomin S., Zelevinsky A., Cluster algebras. II. Finite type classification, Invent. Math. 154 (1) (2003) 63-121. | MR | Zbl

[13] Fomin S., Zelevinsky A., Cluster algebras: Notes for the CDM-03 conference, math.RT/0311493. | Zbl

[14] Geiss C., Leclerc B., Schröer J., Rigid modules over preprojective algebras, math.RT/0503324. | Zbl

[15] Happel D., Triangulated Categories in the Representation Theory of Finite-Dimensional Algebras, London Mathematical Society Lecture Note Series, vol. 119, Cambridge University Press, Cambridge, 1988. | MR | Zbl

[16] Happel D., Rickard J., Schofield A., Piecewise hereditary algebras, London Math. Soc. 20 (1988) 23-28. | MR | Zbl

[17] Hubery A., Acyclic cluster algebras via Ringel-Hall algebras, Preprint available at the author's homepage.

[18] Keller B., Triangulated orbit categories, Doc. Math. 10 (2005) 551-581. | EuDML | MR | Zbl

[19] Keller B., Reiten I., Cluster tilted algebras are Gorenstein and stably Calabi-Yau, math.RT/0512471. | Zbl

[20] Sherman P., Zelevinsky A., Positivity and canonical bases in rank 2 cluster algebras of finite and affine types, Mosc. Math. J. 4 (4) (2004) 947-974, 982. | MR | Zbl

Cité par Sources :