Comptes Rendus
Algèbre, Combinatoire
On the Hochschild homology of singularity categories
Yu Wang1, 2  ; Umamaheswaran Arunachalam3  ; Bernhard Keller4
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, Volume 360 (2022), 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.

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DOI : 10.5802/crmath.318
Classification : 16E35, 16E40, 16E45, 18G80
Yu Wang 1, 2 ; Umamaheswaran Arunachalam 3 ; Bernhard Keller 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {On the {Hochschild} homology of singularity categories},
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Yu Wang; Umamaheswaran Arunachalam; Bernhard Keller. On the Hochschild homology of singularity categories. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 491-496. doi : 10.5802/crmath.318. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.318/

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