JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (4): 1-8.doi: 10.6040/j.issn.1671-9352.0.2024.336

   

Nijenhuis paired Hopf modules and their constructions

ZHANG Liangyun, LIAO Meilin, JIANG Runzi, CAI Mingchao   

  1. College of Science, Nanjing Agricultural University, Nanjing 210095, Jiangsu, China
  • Published:2026-04-08

PDF (PC)

34

Abstract: The concept of Nijenhuis paired Hopf modules is introduced by combining Nijenhuis paired modules with Nijenhuis paired comodules. Nijenhuis paired Hopf modules are then constructed from the antipode and group-like element of a Hopf algebra. The structure theorem for Nijenhuis paired Hopf modules is provided.

Key words: Nijenhuis algebras, Hopf algebras, Nijenhuis paired Hopf modules

CLC Number: 

  • O153
[1] NIJENHUIS A. Xn-1-forming sets of eigenvectors[J]. Indagationes Mathematicae, 1951, 13:200-212.
[2] FRÖLICHER A, NIJENHUIS A. Theory of vector valued differential forms. part I[J]. Indagationes Mathematicae, 1956, 18:338-360.
[3] MAGRI F. A simple model of the integrable Hamiltonian equation[J]. Journal of Mathematical Physics, 1978, 19(5):1156-1162.
[4] GOLUBCHIK I Z, SOKOLOV V V. One more type of classical Yang-Baxter equation[J]. Functional Analysis and Its Applications, 2000, 34:296-298.
[5] GOLUBCHIK I Z, SOKOLOV V V. Generalized operator Yang-Baxter equations, integrable ODEs and nonassociative algebras[J]. Journal of Nonlinear Mathematical Physics, 2000, 7(2):184-197.
[6] BAXTER G. An analytic problem whose solution follows from a simple algebraic identity[J]. Pacific Journal of Mathematics, 1960, 10(3):731-742.
[7] GUO Li, LIN Zongzhu. Representations and modules of Rota-Baxter algebras[J]. Asian Journal of Mathematics, 2021, 25(6):841-870.
[8] LIU Jiefeng,SHENG Yunhe, ZHOU Yanqiu. Nijenhuis operators on n-Lie algebras[J]. Communications in Theoretical Physics, 2016, 10(6):659-670.
[9] SWEEDLER M E. Hopf algebras[M]. New York: Benjamin, 1969.
[10] CARINENA J, GRABOWSKI J, MARMO G. Quantum bi-Hamiltonian systems[J]. International Journal of Modern Physics A, 2000, 15(30):4797-4810.
[11] EBRAHIMI-FARD K. Rota-Baxter algebras and the Hopf algebra of renormalization[D]. Germany: Bonn University, 2006.
[12] FANG Yunfei, WANG Ximu, ZHANG Liangyun. The deformations and constructions of Nijenhuis paired modules[J]. International Electronic Journal of Algebra, 2025, 38:52-69.
[13] GABRIELLA B, FLORIAN N, KORNÈL S. Weak Hopf algebras: I. integral theory and C*-Structure[J]. Journal of Algebra, 1999, 221(2):385-438.
[14] ZHENG Huihui, GUO Li, ZHANG Liangyun. Rota-Baxter paired modules and their constructions from Hopf algebras[J]. Journal of Algebra, 2020, 559:601-624.
[15] ZHENG Huihui, ZHANG Yuxin, ZHANG Liangyun. Rota-Baxter paired comodule and Rota-Baxter paired Hopf module[J]. Colloquium Mathematical, 2021, 168(1):59-83.
[1] 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.
[2] WANG Wei. Hopf algebra structures on unified products and smash coproducts [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 9-13.
[3] 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.
[4] 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.
[5] WANG Sheng-xiang1,2, GUO Shuang-jian2. Hom-Hopf modules for a class of symmetric categories [J]. J4, 2013, 48(4): 40-45.
[6] CHEN Quan-guo, GUO Ji-dong. The Monoidal category of generalized quantum cocommutative coalgebras [J]. J4, 2012, 47(12): 69-71.
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