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The Morita contexts and Galois extensions for weak Hopf group coalgebras. (English) Zbl 1499.16075

Summary: In this paper, we mainly construct a Morita context associated to a weak Hopf group coalgebra and as application we also compute the Morita contexts of weak Hopf group Galois extensions.

MSC:

16T05 Hopf algebras and their applications
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References:

[1] M. Cohen, A Morita context related to finite automorphism group of rings, Pacific J. Math. 98(1) (1982) 37-54. · Zbl 0488.16024
[2] M. Cohen, D. Fischman, Hopf algebra actions, J. Algebra 100 (1986) 363-379. · Zbl 0591.16005
[3] M. Cohen, D. Fischman, S. Montgomery, Hopf Galosi extensions, smash products, and Morita equi valence, J. Algebra 133 (1990) 351-372. · Zbl 0706.16023
[4] G. Bohm, F. Nill, K. Szlachanyi, Weak Hopf Algebras (I): Integral theory and C * -structure , J. Algebra 221 (1999) 385-438. · Zbl 0949.16037
[5] G. Bohm, K. Szlachanyi, Weak Hopf Algebras (II): Representation theory, dimensions, and the Markov trace, J. Algebra 233(1) (2000) 156-212. · Zbl 0980.16028
[6] S. Caenepeel, E. De Groot, Galois theory for weak Hopf algebras, arxiv: math/0406186v1. · Zbl 1146.16018
[7] A. Virelizier, Hopf group-coalgebras, J. Pure Appl. Algebra 171 (2002) 75-122. · Zbl 1011.16023
[8] L.Jia, F. Li, On weak gorup entwining structures, Houston J. Math. 33(3) (2007) 433-451. · Zbl 1134.16015
[9] L.Jia, F. Li, Rudiment of weak Doi-Hopf π-modules, J. Zhejiang Univ. Sci. 6A(Suppl. I) (2005) 144-154. · Zbl 1081.16042
[10] L.Jia, F. Li, Quantum double for a weak T-coalgebra, Algebra Colloquium 17(3) (2010) 475-486. · Zbl 1219.16035
[11] L.Jia, Yetter-Drinfeld π-modules over weak T-coalgebras, Bull. Braz. Math. Soc. 43(3) (2012) 375-396. · Zbl 1258.16037
[12] D.G. Wang, Q.G. Chen, A Maschke type theorem for weak group entwined moudles and applications, Israel Journal of Mathe-matics 204(1) (2014) 329-358. · Zbl 1317.16030
[13] Q.G. Chen, D.G. Wang, M. Liu, Morita theory for group corings, Hacettepe Journal of Mathematics and Statistics 44(6) (2015) 1333-1350. · Zbl 1353.16033
[14] Q.G. Chen, D.G. Wang, Constructing new crossed group categories of weak Hopf group algebras, Mathematica Slovaca 65(3) (2015) 473-492. · Zbl 1363.16045
[15] Q.G. Chen, D.G. Wang, A class of coquasitriangular Hopf group algebras, Communications in algebra 44(1) (2016) 310-335. · Zbl 1367.16030
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