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

Full-text PDF Free Access

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.

**1.**V. G. Drinfeld,*On almost cocommutative Hopf algebras*, Leningrad Math. J.**1**, No.2 (1990), 321-342.**2.**Louis H. Kauffman,*Gauss codes, quantum groups and ribbon Hopf algebras*, Rev. Math. Phys.**5**(1993), no. 4, 735–773. MR**1253734**, 10.1142/S0129055X93000231**3.**Louis H. Kauffman,*Hopf algebras and invariants of 3-manifolds*, J. Pure Appl. Algebra**100**(1995), no. 1-3, 73–92. MR**1344844**, 10.1016/0022-4049(95)98230-4**4.**Robion Kirby and Paul Melvin,*The 3-manifold invariants of Witten and Reshetikhin-Turaev for 𝑠𝑙(2,𝐶)*, Invent. Math.**105**(1991), no. 3, 473–545. MR**1117149**, 10.1007/BF01232277**5.**Richard Gustavus Larson and Moss Eisenberg Sweedler,*An associative orthogonal bilinear form for Hopf algebras*, Amer. J. Math.**91**(1969), 75–94. MR**0240169****6.**K. Liu,*A family of new universal -matrices*, to appear.**7.**David E. Radford,*On Kauffman’s knot invariants arising from finite-dimensional Hopf algebras*, Advances in Hopf algebras (Chicago, IL, 1992) Lecture Notes in Pure and Appl. Math., vol. 158, Dekker, New York, 1994, pp. 205–266. MR**1289427****8.**David E. Radford,*The trace function and Hopf algebras*, J. Algebra**163**(1994), no. 3, 583–622. MR**1265853**, 10.1006/jabr.1994.1033**9.**David E. Radford,*The order of the antipode of a finite dimensional Hopf algebra is finite*, Amer. J. Math.**98**(1976), no. 2, 333–355. MR**0407069****10.**N. Reshetikhin and V. G. Turaev,*Invariants of 3-manifolds via link polynomials and quantum groups*, Invent. Math.**103**(1991), no. 3, 547–597. MR**1091619**, 10.1007/BF01239527**11.**Moss E. Sweedler,*Hopf algebras*, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR**0252485**

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:
http://dx.doi.org/10.1090/S0002-9947-99-02146-7

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