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

DOI:
https://doi.org/10.1090/S0002-9947-99-02146-7

Published electronically:
April 27, 1999

MathSciNet review:
1467472

Full-text PDF

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.**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*, 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 -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 -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**

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:
https://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