Quantum algebras, quantum coalgebras, invariants of 1-1 tangles and knots

Communications in Algebra

Volumn 28, Issue 11, 2000, Pages 5101-5156

  Kauffman, Louis ^a   Radford, David E ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034346946     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1080/00927870008827146     Document Type: Article

References (31)

1. E. Abe, "Hopf Algebras," 74, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, UK, 1980.
2. Yukio Doi, Braided bialgebras and quadratic algebras, Comm. in Algebra 21, (1993), 1731-1749.
3. V. G. Drinfel'd, On almost cocommutative Hopf algebras, Leningrad Math J. (translation) 1 (1990), 321-342.
4. V. G. Drinfel'd, Quantum Groups, Proceedings of the International Congress of Mathematicians, Berkeley, California, USA (1987), 798-820.
5. Louis Kauffman, Gauss Codes, quantum groups and ribbon Hopf algebras, Reviews in Math. Physics 5 (1993), 735-773.
6. Louis Kauffman, "Knots and Physics," World Scientific, Singapore/New Jersey/London/Hong Kong, 1991, 1994.
7. Louis H. Kauffman and David E. Radford, A necessary and sufficient condition for a finite-dimensional Drinfel'd double to be a ribbon Hopf algebra, J. of Algebra 159 (1993), 98-114.
8. Louis H. Kauffman and David E. Radford, A separation result for quantum coalgebras with an application to pointed quantum coalgebras of small dimension, J. of Algebra 225 (2000), 162-200.
9. Louis H. Kauffman and David E. Radford, Invariants of 3-manifolds derived from finite-dimensional Hopf algebras, J. Knot Theory Ramifications 4 (1995), 131-162.
10. Louis H. Kauffman and David E. Radford, On invariants of knots and links which arise from quantum coalgebras, in preparation.
11. Louis H. Kauffman and David E. Radford, Oriented quantum algebras and coalgebras, invariants of knots and links, preprint (2000).
12. Louis H. Kauffman and David E. Radford, Oriented quantum algebras and invariants of knots and links, preprint (2000).
13. Louis H. Kauffman and David E. Radford, Oriented quantum algebras, categories and invariants of knots and links, preprint (2000).
14. Louis H. Kauffman and David E. Radford, Quantum algebra structures on n×n matrices, J. of Algebra 213 (1999), 405-436.
15. Louis H. Kauffman, David E. Radford and Steve Sawin, Centrality and the KRH invariant. J. Knot Theory Ramifications 7 (1998), 571-624.
16. Larry A. Lambe and David E. Radford, "Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An algebraic Approach," Kluwer Academic Publishers, Boston/Dordrecht/London, 1997.
17. S. Majid, Physics for algebraists: non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction, J. of Algebra 129 (1990), 1-91.
18. Shahn Majid, Quasitriangular Hopf algebras and Yang-Baxter equations, Int. J. Mod. Physics A 5 (1990), 1-91.
19. S. Montgomery, "Hopf Algebras and their actions on rings," 82, Regional Conference Series in Mathematics, AMS, Providence, RI, 1993.
20. D. E. Radford, Minimal quasitriangular Hopf algebras, J. Algebra 157 (1993), 285-315.
21. D. E. Radford, On a parameterized family of twist quantum coalgebras and the bracket polynomial, J. of Algebra 225 (2000), 93-123.
22. D. E. Radford, On Kauffman's knot invariants arising from finite-dimensional Hopf algebras. In Advances in Hopf algebras (Chicago, Il 1992), 148 of Lecture Notes in Pure and Applied Math. Series, 205-266. Dekker, New York.
23. D. E. Radford, On the antipode of a quasitriangular Hopf algebra, J. Algebra 151 (1992), 1-11.
24. D. E. Radford, On quantum algebras and coalgebras, oriented quantum algebras and coalgebras, invariants of 1-1 tangles, knots and links, in preparation.
25. D. E. Radford, The order of the antipode of a finite-dimensional Hopf algebra is finite, Amer. J. Math. 98 (1976), 333-355.
26. N. Yu. Reshetikhin and V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), 547-597.
27. N. Yu. Reshetikhin and V. G. Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Physics 127 (1990), 1-26.
28. P. Schauenburg, On coquasitriangular Hopf algebras and the quantum Yang-Baxter equation, Algebra Berichte 67 (1992), 1-76.
29. Yorck Sommerhäuser, On Kaplansky's fifth conjecture, J. of Algebra 204 (1998), 202-224.
30. M. E. Sweedler, "Hopf Algebras," Benjamin, New York, 1969.
31. D. N. Yetter, Quantum groups and representations of monoidal categories, Math. Proc. Camb. Philos. Soc. 108 (1990), 261-290.