no. G5
Algèbre, Combinatoire
On the Hochschild homology of singularity categories
Wang, Yu1, 2 ; Arunachalam, Umamaheswaran3 ; Keller, Bernhard4 
1 Department of Mathematics, Nanjing University, Nanjing 210093, PR China
2 Université Paris Cité, UFR de mathématiques, CNRS IMJ–PRG, 8 place Aurélie Nemours, 75013 Paris, France
3 Department of Mathematics, National Institute of Technology (NIT) Warangal, Warangal, Telangana, 506004, India
4 Université Paris Cité, Sorbonne Université, CNRS IMJ–PRG 8 place Aurélie Nemours, 75013 Paris, France
Comptes Rendus. Mathématique, Tome 360 (2022) no. G5, pp. 491-496.

Let k be an algebraically closed field and A a finite-dimensional k-algebra. In this note, we determine complexes which compute the Hochschild homology of the canonical dg enhancement of the bounded derived category of A and of the canonical dg enhancement of the singularity category of A. As an application, we obtain a new approach to the computation of Hochschild homology of Leavitt path algebras.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.318
Classification : 16E35, 16E40, 16E45, 18G80
Wang, Yu 1, 2 ; Arunachalam, Umamaheswaran 3 ; Keller, Bernhard 4

1 Department of Mathematics, Nanjing University, Nanjing 210093, PR China
2 Université Paris Cité, UFR de mathématiques, CNRS IMJ–PRG, 8 place Aurélie Nemours, 75013 Paris, France
3 Department of Mathematics, National Institute of Technology (NIT) Warangal, Warangal, Telangana, 506004, India
4 Université Paris Cité, Sorbonne Université, CNRS IMJ–PRG 8 place Aurélie Nemours, 75013 Paris, France 
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     title = {On the {Hochschild} homology of singularity categories},
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Wang, Yu; Arunachalam, Umamaheswaran; Keller, Bernhard. On the Hochschild homology of singularity categories. Comptes Rendus. Mathématique, Tome 360 (2022) no. G5, pp. 491-496. doi : 10.5802/crmath.318. http://www.numdam.org/articles/10.5802/crmath.318/

[1] Ara, Pere; Cortiñas, Guillermo Tensor products of Leavitt path algebras, Proc. Am. Math. Soc., Volume 141 (2013) no. 8, pp. 2629-2639 | MR | Zbl

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

[3] Buchweitz, Ragnar-Olaf Maximal Cohen–Macaulay modules and Tate cohomology, Mathematical Surveys and Monographs, 262, American Mathematical Society, 2021 (with appendices by Luchezar L. Avramov, Benjamin Briggs, Srikanth B. Iyengar and Janina C. Letz.) | DOI | Zbl

[4] Chen, Xiao-Wu The singularity category of a quadratic monomial algebra, Q. J. Math, Volume 69 (2018) no. 3, pp. 1015-1033 | DOI | MR | Zbl

[5] Chen, Xiao-Wu; Wang, Zhengfang The dg Leavitt algebra, singular Yoneda category and singularity category (2021) (https://arxiv.org/abs/2109.11278, with an appendix by B. Keller and Yu Wang)

[6] Chen, Xiao-Wu; Yang, Dong Homotopy categories, Leavitt path algebras, and Gorenstein projective modules, Int. Math. Res. Not., Volume 2015 (2015) no. 10, pp. 2597-2633 | DOI | MR | Zbl

[7] Herscovich, Estanislao Hochschild (co)homology of Koszul dual pairs, J. Noncommut. Geom., Volume 13 (2019) no. 1, pp. 59-85 | DOI | MR | Zbl

[8] Keller, Bernhard Deriving DG categories, Ann. Sci. Éc. Norm. Supér., Volume 27 (1994) no. 1, pp. 63-102 | DOI | Numdam | MR | Zbl

[9] 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

[10] Keller, Bernhard On differential graded categories, Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22–30, 2006. Volume II: Invited lectures, European Mathematical Society, 2006, pp. 151-190 | Zbl

[11] Orlov, Dmitri O. Triangulated categories of singularities and D-branes in Landau–Ginzburg models, Tr. Mat. Inst. Steklova, Volume 246 (2004), pp. 240-262 | Zbl

[12] Smith, S. Paul Category equivalences involving graded modules over path algebras of quivers, Adv. Math., Volume 230 (2012) no. 4-6, pp. 1780-1810 | DOI | MR | Zbl

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