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Transactions of the American Mathematical Society

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The trace space and Kauffman's knot invariants

Author: Keqin Liu
Journal: Trans. Amer. Math. Soc. 351 (1999), 3823-3842
MSC (1991): Primary 17B35, 17B37, 17C50, 18A10, 57M25, 57N10
Published electronically: April 27, 1999
MathSciNet review: 1467472
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Abstract | References | Similar Articles | Additional Information

Abstract: The traces in the construction of Kauffman's knot invariants are studied. The trace space is determined for a semisimple finite-dimensional quantum Hopf algebra and the best lower bound of the dimension of the trace space is given for a unimodular finite-dimensional quantum Hopf algebra.

References [Enhancements On Off] (What's this?)

  • 1. V. G. Drinfeld, On almost cocommutative Hopf algebras, Leningrad Math. J. 1, No.2 (1990), 321-342.
  • 2. L. H. Kauffman, Gauss codes, quantum groups and ribbon Hopf algebras, Reviews in Math. Phys. 5, no.4 (1993), 735-773. MR 94k:57013
  • 3. L. H. Kauffman, Hopf algebras and invariants of 3-manifolds, Jour. of Pure and Applied Algebra 100 (1995), 73-92. MR 96h:57014
  • 4. R. Kirby and P. Melvin, The 3-manifold invariants of Witten and Reshetikhin-Turaev for $s\ell l(2, \mathbb{C})$, Inv. Math. 105 (1991), 473-545. MR 92e:57011
  • 5. R. G. Larson and M. E. Sweedler, An associative orthogonal bilinear form for Hopf algebras, Amer. J. Math. 91 (1969), 75-94. MR 39:1523
  • 6. K. Liu, A family of new universal $R$-matrices, to appear.
  • 7. D. E. Radford, On Kauffman's knot invariants arising from finite-dimensional Hopf algebras, Lecture Notes in Pure and Applied Math. 158 (1992), 205-266. MR 96g:57013
  • 8. D. E. Radford, The trace function and Hopf algebras, J. of Algebra. 163 (1994), 583-622. MR 95e:16039
  • 9. D. E. Radford, The order of the antipode of a finite-dimensional Hopf algebra is finite, Amer. J. of Math. 98 (1976), 333-355. MR 53:10852
  • 10. N. Reshetikhin and V.G.Turaev, Invariants of $3$-manifolds via link polynomials and quantum groups, Inv. Math. 103 (1991), 547-597. MR 92b:57024
  • 11. M. E. Sweedler, Hopf algebra, Math. Lecture Notes Series, Benjamin, New York, 1969. MR 40:5705

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Additional Information

Keqin Liu
Affiliation: Department of Mathematics, The University of British Columbia, Vancouver, BC, Canada V6T 1Z2

Received by editor(s): March 25, 1996
Received by editor(s) in revised form: April 21, 1997
Published electronically: April 27, 1999
Article copyright: © Copyright 1999 American Mathematical Society

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