Rota-Baxter Operators on pre-Lie Coalgebras

CHENG Yong-sheng, CUI Ya-xin, DING Wen-jing, WU Lin-li

doi:10.13371/j.cnki.chin.q.j.m.2026.02.003

Chinese Quarterly Journal of Mathematics >

2026 , Vol. 41 >Issue 2: 139 - 146

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2026.02.003

Rota-Baxter Operators on pre-Lie Coalgebras

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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, engages in Lie algebra; CUI Ya-xin (2001-), female, native of Jiaozuo, Henan, master of Henan University, engages in Lie algebra; DING Wen-jing (2001-), native of Luoyang, Henan, master of Henan University, engages in Lie algebra; WU Lin-li (1991-), native of Jiaozuo, Henan, master of Henan University, engages in Lie algebra.

CHENG Yong-sheng (1973-), male, native of Lankao, Henan, professor of Henan University, engages in Lie algebra;

Received date: 2025-07-17

Online published: 2026-06-30

Supported by

Supported by the National Science Foundation of China (Grant Nos. 12371026 and 11771122).

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Abstract

In the present paper, we mainly study Rota-Baxter operators (of weight zero) on pre-Lie coalgebras. In particular, the invertible Rota-Baxter operators on pre-Lie coalgebras is well studied, and some fundamental results of the invertible Rota-Baxter relations and derivations on pre-Lie coalgebras are given. Furthermore, using the Rota-Baxter operators on pre-Lie coalgebras, some new pre-Lie coalgebraic structures are obtained.

Key words： Pre-Lie coalgebras; Rota-Baxter operator; Derivations

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CHENG Yong-sheng, CUI Ya-xin, DING Wen-jing, WU Lin-li . Rota-Baxter Operators on pre-Lie Coalgebras[J]. Chinese Quarterly Journal of Mathematics, 2026 , 41(2) : 139 -146 . DOI: 10.13371/j.cnki.chin.q.j.m.2026.02.003

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