JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (4): 58-66.doi: 10.6040/j.issn.1671-9352.0.2019.409

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Hopf quasicomodules in LLYD Q C M

ZHANG Tao   

  1. School of Mathematics, Southeast University, Nanjing 211189, Jiangsu, China
  • Published:2020-04-09

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Abstract: Let H denote a finite dimensional Hopf coquasigroup in Yetter-Drinfeld quasicomodule category LLYD Q CM, then its linear dual H* is a Hopf quasigroup in LLYD Q CM and also H* has a right H-Hopf quasicomodule structure in LLYD Q CM.

Key words: Hopf(co)quasigroup, Hopf quasicomodule, Yetter-Drinfeld quasimodule, braided monoidal category, duality

CLC Number: 

  • O153.5
[1] DOI Y. Hopf modules in Yetter-Drinfeld catagories[J]. Comm Algebra, 2007, 35(6):3057-3070.
[2] CAENEPEEL S, MILITARU G, ZHU S L. Frobenius and separable functors for generalized module categories and nonlinear equations[M] //Lecture Notes in Mathematics,1787. [S.l.] :Springer, 2002.
[3] WANG S H. Braided monoidal categories associated to Yetter-Drinfeld categories[J]. Comm Algebra, 2002, 30(11):5111-5124.
[4] KLIM J, MAJID S. Hopf quasigroup and the algebraic 7-sphere[J]. J Algebra, 2010, 323:3067-3110.
[5] PÉREZ-IZQUIERDO J M. Algebras, hyperalgebras, nonassociative bialgebras and loops[J]. Adv Math, 2007, 208:834-876.
[6] ALONSO ÁLVAREZ J N, FERNÁNDEZ VILABOA J M, GONZÁLEZ RODRÍGUEZ R, et al. Projections and Yetter-Drinfeld modules over Hopf(co)quasigroups[J].J Algebra, 2015, 443:153-199.
[7] BRZEZINSKI T. Hopf modules and the foundmental theorem for Hopf(co)quasigroups[J]. Intern Elect J Algebra, 2010, 8:114-128.
[8] BRZEZINSSKI T, JIAO Z M. Actions of Hopf quasigroups[J]. Comm Algebra, 2012, 40(2):681-696.
[9] FANG X L, WANG S H. Twisted smash product for Hopf quasigroups[J]. J Southeast Univ(English Ed.), 2011, 27(3):343-346.
[10] ZHANG T, WANG S H, WANG D G. A new approach to braided monoidal categories[J]. J Math Phys, 2019, 60:013510.
[11] SWEEDLER M E. Hopf algebras[M]. New York: Benjamin, 1969.
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