Invariants of links and 3-manifolds obtained from Hopf algebras

Journal of the London Mathematical Society

Volumn 54, Issue 3, 1996, Pages 594-624

  Hennings, Mark ^a  

^a SIDNEY SUSSEX COLLEGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001274392     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/jlms/54.3.594     Document Type: Article

References (25)

1. V. G. DRIN'FELD, 'On almost cocommutative Hopf algebras', Algebra i Analiz 1 (1989) 30-46; Leningrad Math. J. 1 (1990) 321-342.
2. V. G. DRIN'FELD, 'On almost cocommutative Hopf algebras', Algebra i Analiz 1 (1989) 30-46; Leningrad Math. J. 1 (1990) 321-342.
3. R. A. FENN and C. P. ROURKE, 'On Kirby's calculus of links', Topology 18 (1979) 1-15.
4. P. J. FREYD and D. N. YETTER, 'Braided compact closed categories, with applications to low-dimensional topology', Adv. Math. 77 (1989) 156-182.
5. M. A. HENNINGS, 'Hopf algebras and regular isotopy invariants for link diagrams', Math. Proc. Cambridge Philos. Soc. 109 (1991) 59-77.
6. L. H. KAUFFMAN and D. E. RADFORD, 'A necessary and sufficient condition for a Drin'feld double to be a ribbon Hopf algebra', J. Algebra 159 (1993) 98-114.
7. 3', Invent. Math. 45 (1978) 35-56.
8. R. C. KIRBY, The topology of 4-manifolds, Lecture Notes in Mathematics 1374 (Springer, Berlin, 1989).
9. R. G. LARSON, 'Characters of Hopf algebras', J. Algebra 17 (1971) 352-368.
10. R. G. LARSON and D. E. RADFORD, 'Semisimple Hopf algebras', J. Algebra 171 (1995) 5-35.
11. R. G. LARSON and M. E. SWEEDLER, 'An associative orthogonal bilinear form for Hopf algebras', Amer. J. Math. 91 (1969) 75-94.
12. V. LYUBASHENKO and S. MAJID, 'Braided quantum groups and quantum Fourier transform', J. Algebra 166 (1994) 506-528.
13. S. MAJID, 'Quasitriangular Hopf algebras and Yang-Baxter equations', Internat. J. Mod. Phys. A 5 (1990) 1-91.
14. S. MAJID, 'Representation-theoretic rank and double Hopf algebras', Comm. Algebra 18 (1990) 3705-3712.
15. S. MAJID, 'Anyonic quantum groups', Spinors, twistors, Clifford algebras and quantum deformations, Fundamental Theories of Physics 52 (Kluwer Academic, Dordrecht, 1993) 327-336.
16. H. R. MORTON and P. M. STRICKLAND, 'Jones polynomial invariants of knots and satellites', Math. Proc. Cambridge Philos. Soc. 109 (1991) 83-103.
17. H. R. MORTON and P. M. STRICKLAND, 'Satellites and surgery invariants', Knots 90 (de Gruyter, Berlin, 1992) 47-66.
18. W. D. NICHOLLS and M. B. ZOELLER, 'A Hopf algebra freeness theorem', Amer. J. Math. 111 (1989) 381-385.
19. D. E. RADFORD, 'The order of the antipode of a finite-dimensional Hopf algebra is finite', Amer. J. Math. 98 (1976) 333-355.
20. D. E. RADFORD, 'Minimal quasitriangular Hopf algebras', J. Algebra 157 (1993) 285-315.
21. N. Y. RESHETIKHIN and M. A. SEMENOV TIAN-SHANSKII, 'Quantum R-matrices and factorization problems', J. Geom. Phys. 5 (1989) 533-550.
22. N. Y. RESHETIKHIN and V. G. TURAEV, 'Ribbon graphs and their invariants derived from quantum groups', Comm. Math. Phys. 127 (1990) 1-26.
23. N. Y. RESHETIKHIN and V. G. TURAEV, 'Invariants of 3-manifolds via link polynomials and quantum groups', Invent. Math. 103 (1991) 547-597.
24. M. E. SWEEDLER, Hopf algebras (W. A. Benjamin, New York, 1969).
25. E. J. TAFT, 'The order of the antipode of finite-dimensional Hopf algebras', Proc. Nat. Acad. Sci. USA 68 (1971) 2631-2633.