Available in electronic format
Available in print format		 Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

The trace space and Kauffman's knot invariants

Author(s): Keqin Liu
Journal: Trans. Amer. Math. Soc. 351 (1999), 3823-3842.
MSC (1991): Primary 17B35, 17B37, 17C50, 18A10, 57M25, 57N10
Posted: April 27, 1999
Retrieve article in: PDF
This article is available free of charge

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:

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

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 17B35, 17B37, 17C50, 18A10, 57M25, 57N10

Retrieve articles in all Journals with MSC (1991): 17B35, 17B37, 17C50, 18A10, 57M25, 57N10

Additional Information:

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

DOI: 10.1090/S0002-9947-99-02146-7
PII: S 0002-9947(99)02146-7
Received by editor(s): March 25, 1996
Received by editor(s) in revised form: April 21, 1997
Posted: April 27, 1999
Copyright of article: Copyright 1999, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google