Homology of Bihom-Lie Algebras

CHENG Yong-sheng, WANG Meng-ping

doi:10.13371/j.cnki.chin.q.j.m.2022.03.002

Chinese Quarterly Journal of Mathematics >

2022 , Vol. 37 >Issue 3: 237 - 247

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.03.002

Homology of Bihom-Lie Algebras

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School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

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.

Received date: 2022-06-26

Online published: 2022-09-19

Supported by

Supported by the National Science Foundation of China (Grant Nos. 11047030, 11171055).

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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

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CHENG Yong-sheng, WANG Meng-ping . Homology of Bihom-Lie Algebras[J]. Chinese Quarterly Journal of Mathematics, 2022 , 37(3) : 237 -247 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.002

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