Noninvolutory Hopf algebras and $3$-manifold invariants
Greg Kuperberg
Source: Duke Math. J. Volume 84, Number 1
(1996), 83-129.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077243629
Mathematical Reviews number (MathSciNet): MR1394749
Zentralblatt MATH identifier: 0949.57003
Digital Object Identifier: doi:10.1215/S0012-7094-96-08403-3
References
[1] J. W. Barrett and B. W. Westbury, Invariants of piecewise-linear $3$-manifolds, hep-th preprint #9311155.
Mathematical Reviews (MathSciNet): MR1357878
Zentralblatt MATH: 0865.57013
Digital Object Identifier: doi:10.1090/S0002-9947-96-01660-1
JSTOR: links.jstor.org
[2] J. W. Barrett and B. W. Westbury, Spherical categories, hep-th preprint #9310164.
Mathematical Reviews (MathSciNet): MR1686423
Zentralblatt MATH: 0930.18004
Digital Object Identifier: doi:10.1006/aima.1998.1800
[3] S. W. Chung, M. Fukuma, and A. Shapere, Structure of topological lattice field theories in three dimensions, Internat. J. Modern Phys. A 9 (1994), no. 8, 1305–1360.
Mathematical Reviews (MathSciNet): MR95k:57024
Zentralblatt MATH: 0988.57519
Digital Object Identifier: doi:10.1142/S0217751X94000595
[4] R. Dijkgraaf and E. Witten, Topological gauge theories and group cohomology, Comm. Math. Phys. 129 (1990), no. 2, 393–429.
Mathematical Reviews (MathSciNet): MR91g:81133
Zentralblatt MATH: 0703.58011
Digital Object Identifier: doi:10.1007/BF02096988
Project Euclid: euclid.cmp/1104180750
[5] V. Drinfel'd, Quantum groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), Amer. Math. Soc., Providence, RI, 1987, pp. 798–820.
Mathematical Reviews (MathSciNet): MR89f:17017
Zentralblatt MATH: 0667.16003
[6] L. H. Kauffman and D. E. Radford, Invariants of $3$-manifolds derived from finite-dimensional Hopf algebras, hep-th preprint #9406065.
Mathematical Reviews (MathSciNet): MR1321293
Zentralblatt MATH: 0843.57007
Digital Object Identifier: doi:10.1142/S0218216595000077
[7] G. Kuperberg, Invariants of links in $3$-manifolds, in preparation.
[8] G. Kuperberg, Involutory Hopf algebras and $3$-manifold invariants, Internat. J. Math. 2 (1991), no. 1, 41–66.
Mathematical Reviews (MathSciNet): MR91m:57012
Zentralblatt MATH: 0726.57016
Digital Object Identifier: doi:10.1142/S0129167X91000053
[9] R. G. Larson and D. E. Radford, Finite-dimensional cosemisimple Hopf algebras in characteristic $0$ are semisimple, J. Algebra 117 (1988), no. 2, 267–289.
Mathematical Reviews (MathSciNet): MR89k:16016
Zentralblatt MATH: 0649.16005
Digital Object Identifier: doi:10.1016/0021-8693(88)90107-X
[10] G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), no. 2, 447–498.
Mathematical Reviews (MathSciNet): MR90m:17023
Zentralblatt MATH: 0703.17008
Digital Object Identifier: doi:10.2307/1990961
JSTOR: links.jstor.org
[11] D. E. Radford, The order of the antipode of a finite dimensional Hopf algebra is finite, Amer. J. Math. 98 (1976), no. 2, 333–355.
Mathematical Reviews (MathSciNet): MR53:10852
Zentralblatt MATH: 0332.16007
Digital Object Identifier: doi:10.2307/2373888
JSTOR: links.jstor.org
[12] D. E. Radford, The trace function and Hopf algebras, J. Algebra 163 (1994), no. 3, 583–622.
Mathematical Reviews (MathSciNet): MR95e:16039
Zentralblatt MATH: 0801.16039
Digital Object Identifier: doi:10.1006/jabr.1994.1033
[13] N. Yu. Reshetikhin, private communication.
[14] N. Yu. Reshetikhin and V. G. Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990), no. 1, 1–26.
Mathematical Reviews (MathSciNet): MR91c:57016
Zentralblatt MATH: 0768.57003
Digital Object Identifier: doi:10.1007/BF02096491
Project Euclid: euclid.cmp/1104180037
[15] N. Yu. Reshetikhin and V. G. Turaev, Invariants of $3$-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), no. 3, 547–597.
Mathematical Reviews (MathSciNet): MR92b:57024
Zentralblatt MATH: 0725.57007
Digital Object Identifier: doi:10.1007/BF01239527
[16] M. E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969.
Mathematical Reviews (MathSciNet): MR40:5705
Zentralblatt MATH: 0194.32901
[17] V. G. Turaev and H. Wenzl, Quantum invariants of $3$-manifolds associated with classical simple Lie algebras, Internat. J. Math. 4 (1993), no. 2, 323–358.
Mathematical Reviews (MathSciNet): MR94i:57019
Zentralblatt MATH: 0784.57007
Digital Object Identifier: doi:10.1142/S0129167X93000170
Duke Mathematical Journal
