JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (8): 6-14.doi: 10.6040/j.issn.1671-9352.0.2020.619

Previous Articles    

Rota-Baxter paired module system and curved Rota-Baxter paired module system

ZHANG Yu-xin, ZHENG Si-hang, FANG Ying, ZHENG Hui-hui, ZHANG Liang-yun*   

  1. College of Sciences, Nanjing Agricultural University, Nanjing 210095, Jiangsu, China
  • Published:2021-08-09

PDF (PC)

338

Abstract: Firstly, the concepts of Rota-Baxter paired module system and curved Rota-Baxter paired module system are introduced. Then, pre-Lie module and dendriform module are constructed from them. Lastly, Rota-Baxter paired module system and curved Rota-Baxter paired module system are constructed from the integral in semisimple Hopf algebra.

Key words: Rota-Baxter system, Rota-Baxter paired module system, curved Rota-Baxter paired module system, Hopf algebra, pre-Lie module, dendriform module

CLC Number: 

  • O153.3
[1] ROTA G C. Baxter algebras and combinatorial identities Ⅰ,Ⅱ[J]. Bull Am Math Soc, 1969, 75:325-329; 330-334.
[2] GUO Li. An introduction to Rota-Baxter algebra[M] //Surveys of Modern Mathematics 4. Beijing: Higher Education Press, 2012.
[3] GUO Li, LIN Zongzhu. Representations and modules of Rota-Baxter algebras[J/OL]. [2019-05-04]. https://arxiv.org/abs/1905.01531, arXiv:1905.01531.
[4] ZHENG Huihui, GUO Li, ZHANG Liangyun. Rota-Baxter paired modules and their constructions from Hopf algebras[J]. J Algebra, 2020, 559:601-624.
[5] CHAPOTON F, LIVERNET M. Pre-Lie algebras and the rooted trees operad[J]. Int Math Res Not, 2001, 8:395-408.
[6] CONNES A,KREIMER D. Insertion and elimination: the doubly infinite Lie algebra of Feynman graphs[J]. Ann Henri Poincare, 2002, 3:411-433.
[7] AN Huihui, BAI Chengming. From Rota-Baxter algebras to pre-Lie algebras[J]. J Phys A, 2008, 41(1):015201, 19pp.
[8] AGUIAR M. Infinitesimal bialgebras, pre-Lie and dendriform algebras[M] //Lecture Notes in Pure and Appl Math, 237. New York: Dekker, 2004.
[9] BRZEZINSKI T. Rota-Baxter systems, dendriform algebras and covariant bialgebras[J]. J Algebra, 2016, 460:1-25.
[10] 乔宁,房莹,张良云. Sweedler四维Hopf代数上的Poisson代数结构[J].山东大学学报(理学版),2020, 55(12):56-62,68. QIAO Ning, FANG Ying, ZHANG Liangyun. The structure of Poisson algebra on Sweedlers four dimensional Hopf algebra[J]. Journal of Shandong University(Natural Science), 2020, 55(12):56-62,68.
[11] BRZEZINSKI T. Curved Rota-Baxter systems[J]. Bull Belg Math Soc Simon Stevin, 2016, 23(5):713-720.
[12] SWEEDLER M E. Hopf Algebras[J]. New York: Benjamin, 1969.
[1] LI Fang-shu, LI Lin-han, ZHANG Liang-yun. Construction of 3-Leibniz algebras and their Rota-Baxter operators [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(4): 48-53.
[2] SHI Guo-dong. First fundamental theorem and Long dimodules for group-graded Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(4): 25-31.
[3] CHEN Chen, GAO Ying-ying, CHEN Hui-xiang. Lazy 2-cocycles on 9-dimensional Taft algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 73-78.
[4] DAI Li. Z2-extensions of a pointed fusion category and applications [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(12): 93-96.
[5] QIAO Ning, FANG Ying, ZHANG Liang-yun. Structure of Poisson algebras on Sweedler 4-dimensional Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(12): 56-62.
[6] ZHANG Qian, LI Xuan, LI Xin, ZHENG Hui-hui, LI Lin-han, ZHANG Liang-yun. The construct of Rota-Baxter algebra on the Sweedler 4-dimensional Hopf algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 47-52.
[7] CHEN Hua-xi, XU Qing-bing. The fundamental theorem forAMHH in Yetter-Drinfeld module categories [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 107-110.
[8] WANG Wei. Hopf algebra structures on unified products and smash coproducts [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 9-13.
[9] GUO Shuang-jian, LI Yi-zheng. When is BHQ a pre-braided category over quasi-Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 10-15.
[10] YU Xiao-lan. Global dimensions of cocycle deformations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 39-43.
[11] GUO Shuang-jian, LI Yi-zheng. Semisimplicity of the categories of Hom-Yetter-Drinfeld modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 17-23.
[12] JIA Ling, CHEN Xiao-yuan. A duality theorem for a Yetter-Drinfeld Hopf algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 98-101.
[13] YOU Mi-man, ZHAO Xiao-fan. Diagonal crossed products over monoidal Hom-Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 76-80.
[14] 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.
[15] ZHAO Shi-yin1,2, ZHOU Ke-yuan1. The module algebra structures on M2(k) [J]. J4, 2013, 48(8): 24-29.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd