Yetter-Drinfeld Modules forWeak Hom-Hopf Algebras

被引：1
|
作者：
Guo, Shuangjian [1 ]
Ke, Yuanyuan [2 ]
机构：
[1] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Guizhou, Peoples R China
[2] Jianghan Univ, Sch Math & Comp Sci, Wuhan 430056, Hubei, Peoples R China
来源：
FILOMAT | 2017年 / 31卷 / 13期
关键词：
Yetter-Drinfeld module; braided monoidal category; (co)quasitriangular; weak-Hom type entwined-module; LIE-ALGEBRAS; DEFORMATIONS;
D O I：
10.2298/FIL1713069G
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this paper is to define and study Yetter-Drinfeld modules over weak Hom-Hopf algebras. We show that the category HWYDH of Yetter-Drinfeld modules with bijective structure maps over weak Hom-Hopf algebras is a rigid category and a braided monoidal category, and obtain a new solution of quantum Hom-Yang-Baxter equation. It turns out that, If H is quasitriangular (respectively, coquasitriangular) weak Hom-Hopf algebras, the category of modules (respectively, comodules) with bijective structure maps over H is a braided monoidal subcategory of the category HWYDH of Yetter-Drinfeld modules over weak Hom-Hopf algebras.
引用
收藏
页码：4069 / 4084
页数：16
相关论文
共 50 条
  • [31] Symmetric Pairs in Yetter-Drinfeld Categories over Weak Hopf Algebras
    Zhao, Xiaofan
    Liu, Guohua
    Wang, Shuanhong
    COMMUNICATIONS IN ALGEBRA, 2015, 43 (10) : 4502 - 4514
  • [32] CATEGORICAL DUALITY FOR YETTER-DRINFELD ALGEBRAS
    Neshveyev, Sergey
    Yamashita, Makoto
    DOCUMENTA MATHEMATICA, 2014, 19 : 1105 - 1139
  • [33] Hochschild homology of Hopf algebras and free Yetter-Drinfeld resolutions of the counit
    Bichon, Julien
    COMPOSITIO MATHEMATICA, 2013, 149 (04) : 658 - 678
  • [34] Yetter-Drinfeld modules for crossed structures
    Zunino, M
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2004, 193 (1-3) : 313 - 343
  • [35] Parachain Complexes and Yetter-Drinfeld Modules
    Zhu, Haixing
    COMMUNICATIONS IN ALGEBRA, 2016, 44 (01) : 125 - 134
  • [36] Hom-Hopf Algebras Arising From (Co)-Braided Hom-Hopf Algebras
    Jia, Ling
    Chen, Xiaoyuan
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2016, 40 (04) : 511 - 527
  • [37] A GENERALIZED DOUBLE CROSSPRODUCT FOR MONOIDAL HOM-HOPF ALGEBRAS AND THE DRINFELD DOUBLE
    You, Miman
    Wang, Shuanhong
    COLLOQUIUM MATHEMATICUM, 2017, 146 (02) : 213 - 238
  • [38] Yetter-Drinfeld modules over weak braided Hopf monoids and center categories
    Alonso Alvarez, Jose Nicanor
    Gonzalez Rodriguez, Ramon
    Soneira Calvo, Carlos
    ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2014, 30 (04) : 567 - 590
  • [39] The Canonical Isomorphisms in the Yetter-Drinfeld Categories for Dual Quasi-Hopf Algebras
    Ning, Yan
    Lu, Daowei
    Zhao, Xiaofan
    SYMMETRY-BASEL, 2022, 14 (11):
  • [40] Yetter-Drinfeld modules over weak braided Hopf monoids and center categories
    José Nicanor Alonso Álvarez
    Ramón González Rodríguez
    Carlos Soneira Calvo
    Acta Mathematica Sinica, English Series, 2014, 30 : 567 - 590
12345