JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (4): 46-51.doi: 10.6040/j.issn.1671-9352.0.2024.043

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Van den Bergh duality for a class of skew Calabi-Yau algebras

LI Wen, LIU Liyu*   

  1. School of Mathematics, Yangzhou University, Yangzhou 225002, Jiangsu, China
  • Published:2026-04-08

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Abstract: A class of three-dimensional skew Calabi-Yau algebras is constructed using ungraded Ore extensions of the polynomial algebra in two variables. The Nakayama automorphisms of these skew Calabi-Yau algebras are computed, and the Van den Bergh duality between their Hochschild homology and cohomology is established.

Key words: skew Calabi-Yau algebras, Van den Bergh duality, Nakayama automorphisms, Ore extensions

CLC Number: 

  • O154
[1] VAN DEN BERGH M. A relation between Hochschild homology and cohomology for Gorenstein rings[J]. Proceedings of the American Mathematical Society, 1998, 126(5):1345-1348.
[2] BROWN K, HAGAN S, ZHANG J, et al. Connected Hopf algebras and iterated Ore extensions[J]. Journal of Pure and Applied Algebra, 2015, 219(6):2405-2433.
[3] GOODMAN J, KRÄHMER U. Untwisting a twisted Calabi-Yau algebra[J]. Journal of Algebra, 2014, 406:272-289.
[4] LIU Liyu, WANG Shengqiang, WU Quanshui. Twisted Calabi-Yau property of Ore extensions[J]. Journal of Noncommutative Geometry, 2014, 8(2):587-609.
[5] ZHU Can, VAN OYSTAEYEN F, ZHANG Yinhuo. Nakayama automorphisms of double Ore extensions of Koszul regular algebras[J]. Manuscripta Mathematica, 2017, 152:555-584.
[6] SHEN Yuan, ZHOU Guisong, LU Diming. Nakayama automorphisms of twisted tensor products[J]. Journal of Algebra, 2018, 504(2):445-478.
[7] SHEN Yuan, GUO Yang. Nakayama automorphisms of graded Ore extensions of Koszul Artin-Schelter regular algebras[J]. Journal of Algebra, 2021, 579:114-151.
[8] CHAN K, WALTON C, ZHANG J. Hopf actions and Nakayama automorphisms[J]. Journal of Algebra, 2014, 409:26-53.
[9] LÜ Jiafeng, MAO Xuefeng, ZHANG James. Nakayama automorphism and applications[J]. Transactions of the American Mathematical Society, 2014, 369(4):2425-2460.
[10] LÜ Jiafeng, MAO Xuefeng, ZHANG James. The Nakayama automorphism of a class of graded algebras[J]. Israel Journal of Mathematics, 2015, 219(2):707-725.
[11] LIU Liyu, MA Wen. Nakayama automorphisms of Ore extensions over polynomial algebras[J]. Glasgow Mathematical Journal, 2020, 62(3):518-530.
[12] 马雯. 广义Weyl代数上同调的Batalin-Vilkovisky结构[D]. 扬州:扬州大学, 2020. MA Wen. Batalin-Vilkovisky structures on the Hochschild cohomology of generalized Weyl algebras[D]. Yangzhou: Yangzhou University, 2020.
[13] MCCONNELL J C, ROBSON J C. Noncommutative noetherian rings[M]. Chichester: Wiley, 1987.
[1] LU Dao-wei, ZHANG Xiao-hui. Ore extensions of G-cograded multiplier Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(10): 52-58.
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