Comptes Rendus
Article de recherche - Algèbre, Théorie des représentations
Calabi–Yau structures on Drinfeld quotients and Amiot’s conjecture
[Structures Calabi–Yau sur les quotients de Drinfeld et la conjecture d’Amiot]
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 135-142.

En 2009, Claire Amiot a donné une construction de structures de Calabi–Yau sur les quotients de Verdier. Nous esquissons comment la relever au cadre dg. Nous utilisons cette construction comme une étape importante dans l’ébauche de la preuve de la conjecture d’Amiot sur la structure des catégories triangulées 2-Calabi–Yau avec un objet de amas-basculant.

In 2009, Claire Amiot gave a construction of Calabi–Yau structures on Verdier quotients. We sketch how to lift it to the dg setting. We use this construction as an important step in an outline of the proof of her conjecture on the structure of 2-Calabi–Yau triangulated categories with a cluster-tilting object.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.541
Classification : 18E30
Mots clés : Calabi–Yau structure, Verdier quotient, Drinfeld quotient, Amiot’s conjecture

Bernhard Keller 1 ; Junyang Liu 1

1 Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013 Paris, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRMATH_2024__362_G2_135_0,
     author = {Bernhard Keller and Junyang Liu},
     title = {Calabi{\textendash}Yau structures on {Drinfeld} quotients and {Amiot{\textquoteright}s} conjecture},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {135--142},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.541},
     language = {en},
}
TY  - JOUR
AU  - Bernhard Keller
AU  - Junyang Liu
TI  - Calabi–Yau structures on Drinfeld quotients and Amiot’s conjecture
JO  - Comptes Rendus. Mathématique
PY  - 2024
SP  - 135
EP  - 142
VL  - 362
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.541
LA  - en
ID  - CRMATH_2024__362_G2_135_0
ER  - 
%0 Journal Article
%A Bernhard Keller
%A Junyang Liu
%T Calabi–Yau structures on Drinfeld quotients and Amiot’s conjecture
%J Comptes Rendus. Mathématique
%D 2024
%P 135-142
%V 362
%I Académie des sciences, Paris
%R 10.5802/crmath.541
%G en
%F CRMATH_2024__362_G2_135_0
Bernhard Keller; Junyang Liu. Calabi–Yau structures on Drinfeld quotients and Amiot’s conjecture. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 135-142. doi : 10.5802/crmath.541. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.541/

[1] Claire Amiot Cluster categories for algebras of global dimension 2 and quivers with potential, Ann. Inst. Fourier, Volume 59 (2009) no. 6, pp. 2525-2590 | DOI | Numdam | MR | Zbl

[2] Claire Amiot On generalized cluster categories, Representations of algebras and related topics (EMS Series of Congress Reports), European Mathematical Society, 2011, pp. 1-53 | MR | Zbl

[3] Claire Amiot; Osamu Iyama; Idun Reiten; Gordana Todorov Preprojective algebras and c-sortable words, Proc. Lond. Math. Soc., Volume 104 (2012) no. 3, pp. 513-539 | DOI | MR | Zbl

[4] Claire Amiot; Idun Reiten; Gordana Todorov The ubiquity of generalized cluster categories, Adv. Math., Volume 226 (2011) no. 4, pp. 3813-3849 | DOI | MR | Zbl

[5] Michel Van den Bergh Calabi–Yau algebras and superpotentials, Sel. Math., New Ser., Volume 21 (2015) no. 2, pp. 555-603 | DOI | MR | Zbl

[6] Raf Bocklandt Graded Calabi–Yau algebras of dimension 3, J. Pure Appl. Algebra, Volume 212 (2008) no. 1, pp. 14-32 | DOI | MR | Zbl

[7] Harm Derksen; Jerzy Weyman; Andrei Zelevinsky Quivers with potentials and their representations I: Mutations, Mathematica, Volume 14 (2008) no. 1, pp. 59-119 | MR | Zbl

[8] Vladimir Drinfeld DG quotients of DG categories, J. Algebra, Volume 272 (2004) no. 2, pp. 643-691 | DOI | MR | Zbl

[9] Ana Garcia Elsener Monomial Gorenstein algebras and the stably Calabi–Yau property, Algebr. Represent. Theory, Volume 24 (2021) no. 4, pp. 1083-1099 | MR | Zbl

[10] Victor Ginzburg Calabi–Yau algebras | arXiv

[11] Martin Kalck; Dong Yang Relative singularity categories III: Cluster resolutions (2006) | arXiv

[12] Martin Kalck; Dong Yang Relative singularity categories I: Auslander resolutions, Adv. Math., Volume 301 (2016), pp. 973-1021 | DOI | MR | Zbl

[13] Bernhard Keller Invariance and localization for cyclic homology of DG algebras, J. Pure Appl. Algebra, Volume 123 (1998) no. 1-3, pp. 223-273 | DOI | MR | Zbl

[14] Bernhard Keller On the cyclic homology of exact categories, J. Pure Appl. Algebra, Volume 136 (1999) no. 1, pp. 1-56 | DOI | MR | Zbl

[15] Bernhard Keller; Junyang Liu On Amiot’s conjecture (arXiv:2311.06538 [math.RT])

[16] Bernhard Keller; Idun Reiten Cluster-tilted algebras are Gorenstein and stably Calabi–Yau, Adv. Math., Volume 211 (2007) no. 1, pp. 123-151 | DOI | MR | Zbl

[17] Bernhard Keller; Dong Yang Derived equivalences from mutations of quivers with potential, Adv. Math., Volume 26 (2011) no. 3, pp. 2118-2168 | DOI | MR | Zbl

Cité par Sources :

Commentaires - Politique