The Hopf modules category and the Hopf equation

Communications in Algebra

Volumn 26, Issue 10, 1998, Pages 3071-3097

  Militaru, G ^a  

^a UNIVERSITY OF BUCHAREST   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040077238     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1080/00927879808826329     Document Type: Article

References (32)

1. K. Abe, Hopf Algebras, Cambridge University Press, Cambridge, 1977.
2. --algebres, Ann. Sci. Ecole Norm. Sup. 26(1993), 425-488.
3. M. Beattie, S. Dascalescu, L. Grunenfelder, Constructing pointed Hopf algebras by Ore extensions, preprint.
4. S. Caenepeel, G. Militaru, S. Zhu, Crossed modules and Uoi-Hopf modules, Israel J. Math., in press.
5. S. Caenepeel, G. Militaru, S. Zhu, Doi-Hopf modules, Yetter-Drinfel'd modules and Frobenius type properties, Trans. AMS, in press.
6. S. Caenepeel, G. Militaru, S. Zhu, A Maschke type theorem for Doi-Hopf modules, J. Algebra 187 (1997), 388-412.
7. Y. Doi, Unifying Hopf modules, J. Algebra 153 (1992), 373-385.
8. Y. Doi, Algebras with total integral, Comm. Algebra, 13 (1985), 2137-2159.
9. D. Fischman, S. Montgomery, H.-J. Schneider, Frobenius extrusions of subalgebras of Hopf algebras, Trans. AMS, in press.
10. B. Ion, M. Stanciulescu, Several examples of noncommutative and noncocommutative bialgebras arising from the Hopf equation, preprint 1997.
11. I. Kaplansky, Bialgebras, Univiversity of Chicago Press, Chicago, 1975.
12. M. Koppinen, Variations of the smash product with applications to group-graded rings, preprint, 1991.
13. C. Kassel, Quantum groups, Springer Verlag, Berlin, 1995.
14. L.A. Lambe, D. Radford, Algebraic aspects of the quantum Yang-Baxter equation, J. Algebra 54 (1992), 228-288.
15. S. Majid, Foundation of quantum group theory, Cambridge Univ. Press, 1995.
16. S. Majid, Quantum random walks and time reversal, Int. J. Mod. Phys. 8, 4521-4545, 1993.
17. C. Militaru, D. Stefau, Extending modules for Hopf Galois extensions, Comm. Algebra 14 (1994), 5657-5678.
18. G. Militaru, New types of bialgebras arising from the Hopf equation, Comm. Algebra, 26 (1998), 3099-3117
19. S. Montgomery, Hopf algebras and their actions on rings, American Mathematical Society, Providence, 1993.
20. D. Radford, Solutions to the quantum Yang-Baxter equation and the Drinfel'd double, J. Algebra 161 (1993), 20-32.
21. D. Radford, J. Towber, Yetter-Drinfel'd categories associated to an arbitrary bialgebra, J. Pure and Appl. Algebra 87 (1993), 259-279.
22. P. Schauenburg, Hopf module and Yetter-Drinfel'd modules. J. Algebra. 169 (1994), 874-890.
23. H.-J. Schneider, Representation theory for Hopf Galois extensions, Israel J. Math. 70 (1990), 196-231.
24. H.-J. Schneider, Principal homogeneous spaces for arbitrary Hopf algebras, Israel J. Math. 70 (1990), 167-195.
25. H.-J. Schneider, Hopf Galois extensions, crossed products and Clifford theory, Advances in Hopf algebras, edited by J. Bergen, S. Montgomery, (1991), 267-299.
26. D. Stefan, Cohomology of Hopf algebras and the Clifford's extension problem, J. Algebra, 182 (1996), 165-182.
27. M. E. Sweedler, Hopf algebras, Benjamin, New York, 1969.
28. M. Takesaki, Duality and von Neumann algebras, Lecture Notes in Math. vol. 247 (1972), 665-779.
29. M. Takeuchi, Finite dimensional representations of the quantum Lorentz Group, Commun. Math. Phys., 144 (1992). 557-580.
30. A. Van Daele, S. Van Keer. The Yang-Baxter and pentagon equation. Compositio Math., 91 (1994), 201-221.
31. D.N. Yetter, Quantum groups and representations of monoidal categories, Math. Proc. Cambridge Philos. Soc., 108 (1990), 261-290.
32. Y. Zhu, Hopf algebras in prime dimension. International Math. Research Notices, 1 (1994), 53-59.