Homology, Homotopy and Applications

Volume 22 (2020)

Number 2

Koszul duality and the Hochschild cohomology of Artin–Schelter regular algebras

Pages: 181 – 202

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n2.a12


Leilei Liu (Department of Mathematics, Sichuan University, Chengdu, Sichuan, China)


We identify two Batalin–Vilkovisky algebra structures, one obtained by Kowalzig and Krahmer on the Hochschild cohomology of an Artin–Schelter regular algebra with semisimple Nakayama automorphism and the other obtained by Lambre, Zhou and Zimmermann on the Hochschild cohomology of a Frobenius algebra also with semisimple Nakayama automorphism, provided that these two algebras are Koszul dual to each other.


Artin–Schelter algebra, Koszul duality, cohomology, Batalin–Vilkovisky algebra

2010 Mathematics Subject Classification

14A22, 16E40, 16S38

Received 25 January 2019

Received revised 11 June 2019

Accepted 15 October 2019

Published 29 April 2020