Yetter-Drinfeld modules over weak bialgebras

Annali dell'Universita di Ferrara

Volumn 51, Issue 1, 2005, Pages 69-98

  Caenepeel, S ^a   Wang, Dingguo ^b   Yin, Yanmin ^c  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^b QUFU NORMAL UNIVERSITY   (China)

^c SHANDONG JIANZHU UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547247256     PISSN: 04303202     EISSN: 18271510     Source Type: Journal    
DOI: 10.1007/BF02824824     Document Type: Article

References (25)

1. G. Böhm, Doi-Hopf modules over weak Hopf algebras, Comm. Algebra28 (2000), pp. 4687-4698.
2. *-structure, J. Algebra221, (1999), pp. 385-438.
3. R-bialgebras and duality, J. Algebra251 (2002), pp. 279-294.
4. T. Brzeziński-R. Wisbauer, "Corings and comodules", London Math. Soc. Lect. Note Ser., 309, Cambridge University Press, Cambridge, 2003.
5. D. Bulacu-S. Caenepeel-F. Panaite, Yetter-Drinfeld categories for quasi-Hopf algebras, Comm. Algebra, to appear.
6. S. Caenepeel-E. De Groot, Modules over weak entwining structures, Contemp. Math., 267 (2000), pp. 31-54.
7. S. Caenepeel-G. Militaru-S. Zhu, Crossed modules and Doi-Hopf modules, Israel J. Math., 100 (1997), pp. 221-247.
8. Y. Doi, Unifying Hopf modules, J. Algebra153 (1992), pp. 373-385.
9. P. Etingof-D. Nikshych, Dynamical quantum groups at roots of 1, Duke Math. J., 108 (2001), pp. 135-168.
10. T. Hayashi, Quantum group symmetry of partition functions of IRF models and its applications to Jones' index theory, Comm. Math. Phys. 157 (1993), pp. 331-345.
11. A. Joyal-R. Street, Tortile Yang-Baxter operators in tensor categories, J. Pure Appl. Algebra, 71 (1991), pp. 43-51.
12. C. Kassel, "Quantum groups", Grad. Texts Math. 155, Springer Verlag, Berlin, 1995.
13. M. Koppinen, Variations on the smash product with applications to group-graded rings, J. Pure Appl. Algebra, 104 (1995), pp. 61-80.
14. J. H. Lu, Hopf algebroids and quantum groupoids, Intern. J. Math. 7 (1996), pp. 47-70.
15. S. Majid, Representations, duals and quantum doubles of monoidal categories, Rend. Circ. Mat. Palermo (2) Suppl. No. 26 (1991), pp. 197-206.
16. A. Nenciu, The center construction for weak Hopf algebras, Tsukuba J. Mat., 26 (2002), pp. 189-2004.
17. D. Nikshych-V. Turaev-L. Vainerman, Invariants of knots and 3-manifods from quantum groupoids, Topology Appl. 127 (2003), pp. 91-123.
18. D. Nikshych-L. Vainerman, Finite quantum groupoids and their applications in "New directions in Hopf algebras", S. Montgomery and H.-J. Schneider (eds.), Math. Sci. Res. Inst. Publ. 43, Cambridge Univ. Press, Cambridge, 2002, pp. 211-262.
19. A. Ocneanu, Quantum cohomology, quantum groupoids, and subfactors, unpublished talk given at the First Caribbean School of Mathematics and Theoretical Physics, Guadeloupe, 1993.
20. P. Schauenburg, Bialgebras over noncommutative rings and structure theorems for Hopf bimodules, Appl. Categorical Structures, 6 (1998), pp. 193-222.
21. R-algebras), Contemp. Math., 267 (2000), pp. 273-299.
22. P. Schauenburg, Weak Hopf algebras and quantum groupoids, Banach Center Publ., 61 (2003), pp. 171-181.
23. K. Szlachanyi, Finite quantum groupoids and inclusion of finite type, Fields Institute Comm. 30 (2001), pp. 393-407.
24. M. Takeuchi, Groups of algebras over A ⊗ A, J. Math. Soc. Japan, 29 (1977), pp. 459-492.
25. T. Yamanouchi, Duality for generalized Kac algebras and a characterization of finite groupoid algebras, J. Algebra, 163 (1994), pp. 9-50.