Generalized double crossproducts associated with the quantized enveloping algebras

Communications in Algebra

Volumn 26, Issue 1, 1998, Pages 241-291

  Radford, David E ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21944432144     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1080/00927879808826129     Document Type: Article

References (28)

1. V. G. Drinfel'd, Hopf algebras and the quantum Yang-Baxter equation, Soviet Math. Dokl. 32 (1985), 254-258.
2. V. G. Drinfel'd, Quantum groups, Procedings of the International Congress of Mathematicians, Berkeley, California, USA (1987), 798-820.
3. q(g) and the quantum Yang-Baxter equation, Letters in Math. Physics 10 (1985), 63-69.
4. Michio Jimbo, Introduction to the quantum Yang-Baxter equation Int. J. mod. Phy. A 4 (1989), 3259-3777.
5. Joyal and Street, Braided tensor categories, Adv. Math. 102 (1993), 20-78.
6. J. Humphreys, "Introduction to Lie Algebras and Representation Theory," Springer Verlag, New York, 1987.
7. Victor Kac, "Infinite Dimensional Lie Algebras," Cambridge University Press, New York, 1985.
8. R. Kirby and P. Melvin, On the 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C), Invent. Math. 105 (1991), 473-545.
9. P. P. Kurlish and N. Yu. Reshetihkin, The quantum linear problem for sine-Gordon equation and higher representations, LOMI 101 (1980), 101-110.
10. Larry Lambe and David E. Radford, Algebraic aspects of the quantum-Yang Baxter equation, J. of Algebra 154 (1993), 228-288.
11. G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), 447-498.
12. G. Lusztig, Modular representations and quantum groups, Contemp. Math. AMS 82 (1989), 59-77.
13. G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math. 70 (1988), 237-249.
14. S. Majid, Doubles of quasitriangular Hopf algebras, Comm. in Alg. 19 (1991), 3061-3073.
15. S. Majid, Physics for algebraists: non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction, J. of Algebra 129 (1990), 1-91.
16. S. Majid, Quasitriangular Hopf algebras and Yang-Baxter equations, Int. J. Mod. Physics A 5 (1990), 1-91.
17. S. Majid, Sequences of bicrossproduct and double crossproduct Hopf algebras, talk at Int. Conf. Hopf Alg., Beer Sheva, Israel (1989).
18. C1/2•. In Quantum deformations of algebras and their representations (Ramat-Gan, 1991/1992; Rehovot, 1991/1992), 7 Israel Math. Conf. Proc., 143-170. Bar-Ilan Univ., Ramat-Gan.
19. D. E. Radford, Minimal quasitriangular Hopf algebras, J. of Algebra 157 (1993), 285-315.
20. D. E. Radford, Solutions to the quantum Yang-Baxter equation and the Drinfel'd double, J. Algebra 161 (1993), 20-32.
21. D. E. Radford and J. Towber, Yetter-Drinfel'd categories associated to an arbitrary bialgebra, J. Pure and Applied Math. 87 (1993), 259-279.
22. N. Yu. Reshetikhin and V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), 547-597.
23. N. Yu. Reshetikhin and V. G. Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990), 1-26.
24. M. Rosso, Finite-dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra, Comm. Math. Physics 117 (1988), 581-593.
25. M. E. Sweedler, "Hopf Algebras," Mathematics Lecture Notes Series, Benjamin, New York, 1969.
26. Earl J. Taft, The order of the antipode of a finite-dimensional Hopf algebra, Proc. Nat. Acad. Sci. USA 68 (1971), 2631-2633.
27. David N. Yetter, Quantum groups and representations of monoidal categories, Math. Proc. Camb. Phil. Soc. 108 (1990), 261-290.
28. Andre V. Zelevinsky, "Representation Theory of Finite Classical Groups: a Hopf Algebra Approach," Springer Verlag, New York, 1981.