Cross product bialgebras, I

Journal of Algebra

Volumn 219, Issue 2, 1999, Pages 466-505

  Bespalov, Yuri ^a   Drabant, Bernhard ^b  

^a BOGOLYUBOV INSTITUTE FOR THEORETICAL PHYSICS   (Ukraine)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033567761     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1999.7896     Document Type: Article

References (38)

1. M. Beattie, S. Dǎscǎlescu, and, L. Grünenfelder, Constructing pointed Hopf algebras by Ore extensions, preprint, 1998.
2. Yu. Bespalov, Hopf algebras: Bimodules, crossproducts, differential calculus, Preprint ITP-93-57E, 1993.
3. Bespalov Yu. Crossed modules and quantum groups in braided categories. Appl. Categ. Structures. 5:1997;155-204.
4. Bespalov Yu., Drabant B. Hopf (bi-)modules and crossed modules in braided categories. J. Pure Appl. Algebra. 123:1998;105-129.
5. Yu. Bespalov and B. Drabant, Differential calculus in braided tensor categories, Preprint q-alg/9703036, 1997; also, Bicovariant differential calculi and cross products on braided Hopf algebras, in "Quantum Groups and Quantum Spaces" (R. Budzynski et al., Eds.), Banach Center Publications, Vol. 40, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 1997.
6. Yu. Bespalov and B. Drabant, Differential calculus in braided tensor categories, Preprint q-alg/9703036, 1997; also, Bicovariant differential calculi and cross products on braided Hopf algebras, in "Quantum Groups and Quantum Spaces" (R. Budzynski et al., Eds.), Banach Center Publications, Vol. 40, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 1997.
7. Yu. Bespalov, and, B. Drabant, Cross product bialgebras - Part II, Preprint DAMTP-98-117, 1998.
8. Blattner R. J., Cohen M., Montgomery S. Crossed products and inner actions of Hopf algebras. Trans. Amer. Math. Soc. 298:1986;671-711.
9. Brzezinski T. Crossed products by a coalgebra. Comm. Algebra. 25:1997;3551-3575.
10. S. Caenepeel, B. Ion, G. Militaru, and, S. Zhu, Smash biproducts of algebras and coalgebra, preprint, 1998.
11. Chari V., Pressley A. Quantum Groups. 1994;Cambridge Univ. Press, Cambridge.
12. Doi Y., Takeuchi M. Cleft comodule algebras for a bialgebra. Comm. Algebra. 14:1986;801-818.
13. Drinfel'd V. G. Quasi-Hopf algebra. Leningrad Math. J. 1:1990;1419-1457.
14. Freyd P., Yetter D. Braided compact closed categories with applications to low dimensional topology. Adv. Math. 77:1989;156-182.
15. Joyal A., Street R. Braided tensor categories. Macquarie Math. Reports. 860081:1986.
16. Joyal A., Street R. Braided tensor categories. Adv. Math. 102:1993;20-78.
17. Kassel C. Quantum Groups. Graduate Texts in Mathematics. 155:1995;Springer-Verlag, Berlin/New York.
18. Lusztig G. Introduction to Quantum Groups. Progress in Mathematics. 110:1993;Birkhäuser, Boston.
19. Lyubashenko V. V. Tangles and Hopf algebras in braided categories. J. Pure Appl. Algebra. 98:1995;245.
20. Lyubashenko V. V. Modular transformations for tensor categories. J. Pure Appl. Algebra. 98:1995;279.
21. Mac Lane S. Natural associativity and commutativity. Rice University Studies. 49:1963;28.
22. Mac Lane S. Categories. For the Working Mathematician. Graduate Texts in Mathematics. 5:1972;Springer-Verlag, Berlin/New York.
23. Majid S. Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction. J. Algebra. 130:1990;17-64.
24. Majid S. Braided groups. J. Pure Appl. Algebra. 86:1993;187.
25. Majid S. Dobrev V. K., Doebner H.-D., Ushveridze A. G., Cross product quantization, nonabelian cohomology and twisting of Hopf algebras. 1995;13-41 World Scientific, Singapore.
26. Majid S. Some remarks on the quantum double. Proceedings of the 3rd Colloquium on Quantum Groups (Prague 1994). Czech. J. Phys. 44:1994;1059-1071.
27. q(g). Math. Proc. Cambridge Philos. Soc. 125:1999;151-192.
28. Montgomery S. Hopf Algebras and Their Actions on Rings. CBMS. 82:1992;Am. Math. Soc. Providence.
29. Radford D. E. The structure of Hopf algebras with a projection. J. Algebra. 92:1985;322.
30. Radford D. E. On Kauffman's knot invariants arising from finite-dimensional Hopf algebras. Bergen J., Montgomery S., Advances in Hopf Algebras. Lecture Notes in Pure and Applied Mathematics. 158:1994;205-266 Dekker, New York.
31. Reshetikhin N. Yu., Turaev V. G. Ribbon graphs and their invariants derived from quantum groups. Comm. Math. Phys. 127:1990;1.
32. Reshetikhin N. Yu., Turaev V. G. Invariants of 3-manifolds via link polynomials and quantum groups. Invent. Math. 103:1991;547.
33. Schauenburg P. Hopf modules and Yetter-Drinfel'd modules. J. Algebra. 169:1994;874-890.
34. Sommerhäuser Y. Deformed enveloping algebras. New York J. Math. 2:1996;35-58.
35. Sweedler M. E. Hopf Algebras. 1969;Benjamin, New York.
36. Turaev V. G. Quantum invariants of knots and 3-manifolds. Studies in Mathematics. 18:1994;de Gruyter, Berlin/New York.
37. Woronowicz S. L. Differential calculus on compact matrix pseudogroups (quantum groups). Comm. Math. Phys. 122:1989;125-170.
38. Yetter D. Quantum groups and representations of monoidal categories. Math. Proc. Cambridge Philos. Soc. 108:1990;261-290.