Chinese Quarterly Journal of Mathematics ›› 2022, Vol. 37 ›› Issue (3): 237-247.doi: 10.13371/j.cnki.chin.q.j.m.2022.03.002

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Homology of Bihom-Lie Algebras

  

  1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
  • Received:2022-06-26 Online:2022-09-25 Published:2022-09-19
  • Contact: CHENG Yong-sheng (1973-), male, native of Lankao, Henan, professor of Henan University, Ph.D., engages in Lie algebra and its representation E-mail: yscheng@henu.edu.cn.
  • About author: CHENG Yong-sheng (1973-), male, native of Lankao, Henan, professor of Henan University, Ph.D., engages in Lie algebra and its representation; WANG Meng-ping (1991-), female, native of Zhoukou, Henan, master of Henan University, engages in Lie algebra.
  • Supported by:
    Supported by the National Science Foundation of China (Grant Nos. 11047030, 11171055).

Abstract:  The purpose of this paper is to define Hochschild type homology of Bihom-
associative algebras and Chevalley-Eilenberg type homology of Bihom-Lie algebras with
non-trivial coefficients in their bimodules respectively. In particular, we give their low
order homology in detail.

Key words: Bihom-Lie algebras, Bihom-bimodules, Chain complex, Homology

CLC Number: