no. G2
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]
Keller, Bernhard1  ; Liu, Junyang1
1Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013 Paris, France
Comptes Rendus. Mathématique, Tome 362 (2024) no. G2, pp. 135-142

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.

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.

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DOI : 10.5802/crmath.541
Classification : 18E30
Keywords: Calabi–Yau structure, Verdier quotient, Drinfeld quotient, Amiot’s conjecture

Keller, Bernhard  1   ; Liu, Junyang  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
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Keller, Bernhard; Liu, Junyang. Calabi–Yau structures on Drinfeld quotients and Amiot’s conjecture. Comptes Rendus. Mathématique, Tome 362 (2024) no. G2, pp. 135-142. doi: 10.5802/crmath.541

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

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

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

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

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

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

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

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

[10] Ginzburg, Victor Calabi–Yau algebras | arXiv

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

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

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

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

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

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

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