### Quasidimodule algebras over Hopf quasigroups and Yetter-Drinfeld quasimodule algebras

WU Zi-juan, CHEN Yuan-yuan, ZHANG Liang-yun*

1. College of Science, Nanjing Agricultural University, Nanjing 210095, Jiangsu, China
• Received:2016-01-19 Online:2016-10-20 Published:2016-10-17

Abstract: A sufficient and necessary condition for a Long skew Hopf quasigroup to be a quasidimodule algebra is given, and the relation between the braided Hopf quasigroup and the Yetter-Drinfeld quasimodule algebra is studied. At the end, the quantization of Long skew Hopf quasigroups is constructed by Harrison 2-cocycle, and the conclusion for a quantized Long skew Hopf quasigroup to be a quasidimodule algebras is proved.

CLC Number:

• O153.3
 [1] KLIM J, MAJID S. Hopf quasigroups and the algebraic 7-sphere[J]. Joural of Algebra, 2010, 323(11):3067-3110.[2] ZHANG Liangyun. Long bialgebras, dimodule algebras and quantum Yang-Baxter modules over Long bialgebras[J]. Acta Mathematica Sinica, 2006, 22(4):1261-1270.[3] CAO Xuexia, ZHANG Liangyun. Quantization of dimodule algebras and Quantum Yang-Baxter module algebras[J]. Joural of Mathmatical Research and Exposition, 2010, 30(4):725-733.[4] 焦争鸣,王艳玲. Hopf拟群的代数形变[J].河南师范大学学报(自然科学版),2013,41(6):9-12. JIAO Zhengming, WANG Yanling. Algebra deformation of Hopf quasigroup[J]. Joural of Henan Normal University(Nature Science Edition), 2013, 41(6):9-12.[5] JIAO Zhengming, ZHAO Xiaofang. Almost cocommutative and quasitriangular Hopf coquasigroups[J]. Journal of Algebra and its Applications, 2014, 13(6):1-14.[6] SWEEDLER M E. Hopf Algebras[M]. New York: Benjamin, 1969: 3-90.[7] MONTGOMERY S. Hopf algebras and their actions on rings[M]. Rhode Island: American mathematical society providence, 1993: 1-40.[8] BRZEZINSKI T. Hopf modules and the fundamental theorem for Hopf(co)quasigroups[J]. International Electronic Journal of Algebra, 2010, 8:114-128.[9] XIAO Lifang, TORRECILLAS B. Twisted smash products and L-R smash products for biquasimodule Hopf quasigroups[J]. Communications in Algebra, 2014, 42(10):4204-4234.
 [1] WU Xiao-ying, WANG Fang-gui. Graded version of Enochs theorem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 22-26. [2] CHENG Cheng, ZOU Shi-jia. Irreducible splitting trace module of a class of Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 11-15. [3] ZHU Lin. Separated monic representations of quivers of type A4and RSS equivalences [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 1-8. [4] 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. [5] LU Dao-wei, WANG Zhen. L-R smash product for bialgebroids [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 32-35. [6] LI Jin-lan, LIANG Chun-li. Strongly Gorenstein C-flat modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 25-31. [7] WANG Hui-xing, CUI Jian, CHEN Yi-ning. Nil *-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 16-24. [8] SUN Yan-zhong, YANG Xiao-yan. Gorenstein AC-projective modules with respect to a semidualizing module [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 31-35. [9] MA Xin, ZHAO You-yi, NIU Xue-na. Homology resolutions and homological dimensions of complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 18-23. [10] . Gelfand-Krillov dimension of quantized enveloping algebra Uq(An) [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 12-17. [11] CHEN Xiu-li, CHEN Jian-long. Homological dimensions with respect to semidualizing modules and excellent extensions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 85-89. [12] 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. [13] LU Qi, BAO Hong-wei. ZWGP-injectivity and nonsingularity of rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 19-23. [14] GAO Han-peng, YIN Xiao-bin. On strongly g(x)-J-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 24-29. [15] WANG Yao, ZHOU Yun, REN Yan-li. Strongly 2-good Rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 14-18.
Viewed
Full text

Abstract

Cited

Shared
Discussed