FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS

被引：3
|
作者：
Zhang, Xigou [1 ]
Gao, Xing [2 ]
Guo, Li [3 ]
机构：
[1] Jiangxi Normal Univ, Coll Math & Informat Sci, Nanchang 330022, Jiangxi, Peoples R China
[2] Lanzhou Univ, Key Lab Appl Math & Complex Syst, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
[3] Rutgers Univ Newark, Dept Math & Comp Sci, Newark, NJ 07102 USA
来源：
INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA | 2019年 / 25卷
基金：
中国国家自然科学基金;
关键词：
Modified Rota-Baxter algebra; Rota-Baxter algebra; Hopf algebra; bracketed word; cocycle; ASSOCIATIVE ALGEBRAS; O-OPERATORS; RENORMALIZATION;
D O I：
10.24330/ieja.504101
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The notion of a modified Rota-Baxter algebra comes from the combination of those of a Rota-Baxter algebra and a modified Yang-Baxter equation. In this paper, we first construct free modified Rota-Baxter algebras. We then equip a free modified Rota-Baxter algebra with a bialgebra structure by a cocycle construction. Under the assumption that the generating algebra is a connected bialgebra, we further equip the free modified Rota-Baxter algebra with a Hopf algebra structure.
引用
下载
收藏
页码：12 / 34
页数：23
相关论文
共 50 条
  • [41] Rota-Baxter algebras and new combinatorial identities
    Kurusch, Ebrahimi-Fard
    Gracia-Bondia, Jose M.
    Patras, Frederic
    LETTERS IN MATHEMATICAL PHYSICS, 2007, 81 (01) : 61 - 75
  • [42] Rota-Baxter operators on involutive associative algebras
    Das, Apurba
    ACTA SCIENTIARUM MATHEMATICARUM, 2021, 87 (3-4): : 349 - 366
  • [43] RELATIVE ROTA-BAXTER OPERATORS AND TRIDENDRIFORM ALGEBRAS
    Bai, Chengming
    Guo, Li
    Ni, Xiang
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2013, 12 (07)
  • [44] Factorizable Lie Bialgebras, Quadratic Rota-Baxter Lie Algebras and Rota-Baxter Lie Bialgebras
    Lang, Honglei
    Sheng, Yunhe
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2023, 397 (02) : 763 - 791
  • [45] Polylogarithms and multiple zeta values from free Rota-Baxter algebras
    Guo Li
    Zhang Bin
    SCIENCE CHINA-MATHEMATICS, 2010, 53 (09) : 2239 - 2258
  • [46] Grobner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras
    Bokut, L. A.
    Chen, Yuqun
    Qiu, Jianjun
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2010, 214 (01) : 89 - 100
  • [47] Polylogarithms and multiple zeta values from free Rota-Baxter algebras
    GUO Li1
    2Department of Mathematics and Computer Science
    3Yangtze Center of Mathematics
    Science China Mathematics, 2010, 53 (09) : 2239 - 2258
  • [48] Polylogarithms and multiple zeta values from free Rota-Baxter algebras
    Li Guo
    Bin Zhang
    Science China Mathematics, 2010, 53 : 2239 - 2258
  • [49] Matching relative Rota-Baxter algebras, matching dendriform algebras and their cohomologies
    Mandal, Ramkrishna
    Das, Apurba
    COMMUNICATIONS IN ALGEBRA, 2024,
  • [50] Post-Hopf algebras, relative Rota-Baxter operators and solutions to the Yang-Baxter equation
    Li, Yunnan
    Sheng, Yunhe
    Tang, Rong
    JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2024, 18 (01) : 605 - 630
12345