Integrals for (dual) quasi-Hopf algebras. Applications

Journal of Algebra

Volumn 266, Issue 2, 2003, Pages 552-583

  Bulacu, D ^a   Caenepeel, S ^b  

^a UNIVERSITY OF BUCHAREST   (Romania)

^b VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042658335     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(03)00175-3     Document Type: Article

References (23)

1. E. Abe, Hopf Algebras, Cambridge University Press, Cambridge, 1977.
2. M. Beattie, S. Dǎscǎlescu, Ş. Raianu, Galois extensions for co-Frobenius Hopf algebras, J. Algebra 198 (1997) 164-183.
3. M. Beattie, S. Dǎscǎlescu, L. Grünenfelder, C. Nǎstǎsescu, Finiteness conditions, co-Frobenius Hopf algebras and quantum groups, J. Algebra 200 (1998) 312-333.
4. D. Bulacu, E. Nauwelaerts, Relative Hopf modules for (dual) quasi-Hopf algebras, J. Algebra 229 (2000) 632-659.
5. D. Bulacu, E. Nauwelaerts, Radford's biproduct for quasi-Hopf algebras and bosonization, J. Pure Appl. Algebra 174 (2002) 1-42.
6. S. Dǎscǎlescu, C. Nǎstǎsescu, B. Torrecillas, Co-Frobenius Hopf algebras: Integrals, Doi-Koppinen modules and injective objects, J. Algebra 220 (1999) 542-560.
7. S. Dǎscǎlescu, C. Nǎstǎsescu, Ş. Raianu, Hopf Algebras: An Introduction, in: Monographs Textbooks in Pure Appl. Math., Vol. 235, Dekker, New York, 2001.
8. V.G. Drinfel'd, Quasi-Hopf algebras, Leningrad Math. J. 1 (1990) 1419-1457.
9. F. Hausser, F. Nill, Diagonal crossed products by duals of quasi-quantum groups, Rev. Math. Phys. 11 (1999) 553-629.
10. F. Hausser, F. Nill, Doubles of quasi-quantum groups, Comm. Math. Phys. 199 (1999) 547-589.
11. F. Hausser, F. Nill, Integral theory for quasi-Hopf algebras, math.QA/9904164.
12. C. Kassel, Quantum Groups, in: Graduate Texts in Math., Vol. 155, Springer-Verlag, Berlin, 1995.
13. R. Larson, M. Sweedler, An associative orthogonal bilinear form for Hopf algebras, Amer. J. Math. 91 (1969) 75-94.
14. S. Majid, Foundations of Quantum Group Theory, Cambridge University Press, Cambridge, 1995.
15. S. Montgomery, Hopf Algebras and Their Actions on Rings, American Mathematical Society, Providence, RI. 1993.
16. F. Panaite, F.V. Oystaeyen, Existence of integrals for finite dimensional quasi-Hopf algebras, Bull. Belg. Math. Soc. Simon Stevin 7 (2000) 261-264.
17. D.E. Radford, Finiteness conditions for a Hopf algebra with a non-zero integral, J. Algebra 46 (1977) 189-195.
18. Ş. Raianu, An easy proof for uniqueness of integrals, in: S. Caenepeel, F. Van Oystaeyen (Eds.), Hopf Algebras and Quantum Groups, in: Lecture Notes Pure Appl. Math., Vol. 209, Dekker, New York, 2000, pp. 237-240.
19. P. Schauenburg, Two characterizations of finite quasi-Hopf algebras, math.QA/0207069.
20. J.B. Sullivan, The uniqueness of integrals for Hopf algebras and some existence theorems of integrals for cocommutative Hopf algebras, J. Algebra 19 (1971) 426-440.
21. M.E. Sweedler, Hopf Algebras, Benjamin, New York, 1969.
22. D. Ştefan, The uniqueness of integrals. A homological approach, Comm. Algebra 23 (1995) 1657-1662.
23. A. Van Daele, The Haar measure on finite quantum groups, Proc. Amer. Math. Soc. 125 (1997) 3489-3500.