Weak C-cleft extensions, weak entwining structures and weak Hopf algebras

Journal of Algebra

Volumn 284, Issue 2, 2005, Pages 679-704

  Alonso Alvarez J N ^a   Fernandez Vilaboa J M ^b   Gonzalez Rodriguez R ^a   Rodriguez Raposo A B ^b  

^a UNIVERSITY OF VIGO   (Spain)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Weak C cleft extension; Weak entwining structure; Weak Hopf algebra

Indexed keywords

EID: 12344281911     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2004.07.043     Document Type: Article

References (29)

1. J.N. Alonso Álvarez J.M. Fernández Vilaboa Cleft extensions in braided categories Comm. Algebra 28 7 2000 3185-3196
2. J.N. Alonso Álvarez R. González Rodríguez J.M. Fernández Vilaboa M.P. López López E. Villanueva Novoa Weak Hopf algebras with projection and weak smash bialgebra structures J. Algebra 269 2 2003 701-725
3. J.N. Alonso Álvarez R. González Rodríguez Crossed products for weak Hopf algebras with coalgebra splitting J. Algebra 281 2 2004 731-752
4. J.N. Alonso Álvarez, J.M. Fernández Vilaboa, R. González Rodríguez, A.B. Rodríguez Raposo, Weak C-cleft extensions and weak Galois extensions, preprint, 2004
5. Y. Bespalov Crossed modules and quantum groups in braided categories Appl. Categ. Structures 5 2 1997 155-204
6. Y. Bespalov B. Drabant Cross product bialgebras I J. Algebra 219 2 1999 466-505
7. Y. Bespalov B. Drabant Cross product bialgebras II J. Algebra 240 2 2001 445-504
8. Y. Bespalov B. Drabant Hopf (bi-)modules and crossed modules in braided monoidal categories J. Pure Appl. Algebra 123 1998 105-129
9. R. Blattner M. Cohen S. Montgomery Crossed products and inner actions of Hopf algebras Trans. Amer. Math. Soc. 298 2 1986 671-711
10. G. Böhm Doi-Hopf modules over weak Hopf algebras Comm. Algebra 28 2000 4687-4698
11. G. Böhm F. Nill K. Szlachányi Weak Hopf algebras, I: Integral theory and C * -structure J. Algebra 221 2 1999 385-438
12. G. Böhm K. Szlachányi Weak Hopf algebras, II: Representation theory, dimensions and the Markov trace J. Algebra 233 2000 156-212
13. T. Brzeziński Crossed products by a coalgebra Comm. Algebra 25 11 1997 3551-3575
14. T. Brzeziński On modules associated to coalgebra Galois extensions J. Algebra 215 1999 290-317
15. T. Brzeziński S. Majid Coalgebra bundles Comm. Math. Phys. 191 1998 467-492
16. S. Caenepeel E. de Groot Modules over weak entwining structures Contemp. Math. 267 2000 31-54
17. Y. Doi On the structure of relative Hopf modules Comm. Algebra 11 3 1983 243-255
18. Y. Doi Unifying Hopf modules J. Algebra 153 2 1992 373-385
19. Y. Doi M. Takeuchi Cleft comodule algebras for a bialgebra Comm. Algebra 14 1986 801-817
20. J.M. Fernández Vilaboa, A.B. Rodríguez Raposo, Entwined modules and (co)cleft extensions, preprint, 2004
21. A. Joyal R. Street Braided monoidal categories Adv. Math. 102 1993 20-78
22. M. Koppinen Variations in the smash product with applications to group-graded rings J. Pure Appl. Algebra 104 1 1995 61-80
23. H.F. Kreimer M. Takeuchi Hopf algebras and Galois extensions of an algebra Indiana Univ. Math. J. 30 1981 675-691
24. S. Majid Cross products by braided groups and bosonization J. Algebra 163 1 1994 165-190
25. D. Nikshych L. de Vainerman Finite quantum groupoids and their applications in: New Directions in Hopf Algebras in: MSRI Publ. vol. 43 2002 211-262
26. D. Nikshych V. Turaev L. de Vainerman Invariants of knots and 3-manifolds from quantum groupoids Topology Appl. 127 2003 91-123
27. D.E. Radford The structure of Hopf algebras with a projection J. Algebra 92 1985 322-347
28. D.E. Radford J. Towber Yetter-Drinfeld categories associated to an arbitrary bialgebra J. Pure Appl. Algebra 87 1993 259-279
29. D.N. Yetter Quantum groups and representations of monoidal categories Math. Proc. Cambridge Philos. Soc. 108 2 1990 261-290