Ribbon graphs and their invaraints derived from quantum groups
Article
- 423 Downloads
- 407 Citations
Abstract
The generalization of Jones polynomial of links to the case of graphs inR3 is presented. It is constructed as the functor from the category of graphs to the category of representations of the quantum groups.
Keywords
Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.[Br] Brejxxxxxxxxxxxer, M.R., Moody, R.V., Patera, J.: Tables of dominant weight multiplicites for representation of simple Lie groups. New York: Dekker 1984.Google Scholar
- 2.[D] Deling, P., Milne, J.S.: Tannakian Categories in Hodge cicles motives and simura varieties. Lecture Notes ion Mathematics, vol 900. Berlin, Heidelberg, New York: Springer 1982Google Scholar
- 3.[Dr1] Drinfeld, V.G.: Proceedings of the International Congres of Mathematics, vol. 1, p. 798–820. Berkeley, California: New York: Academic Press 1986)Google Scholar
- 4.[Dr2] Drinfeld, V.G.: Quasicommutative Hopf algebras. Algebra and Anal.1 (1989)Google Scholar
- 5.[FRT] Faddeev, L., Reshetikhin, N., Takhtajan, L.: Quantized Lie Groups and Lie algebras. LOMI-preprint, E-14-87, 1987, LeningradGoogle Scholar
- 6.[FY] Freyd, P.J., Yetter, D.N.: Braided compact closed categories with applications to low dimensional topology. Preprint (1987)Google Scholar
- 7.[JS] Joyal, A., Street, R.: Braied Manoidal categories. Macquarie Math. Reports. Report No. 860081 (1986)Google Scholar
- 8.[JO] Jones, V.F.R.: A polynomial invariant of Knots via von Neumann algebras. Bull. Am. Math. Soc.12, 103–111 (1985)Google Scholar
- 9.[KT] Tsuchiya, A., Kanlie, Y.: Vertex operators in the conformal field theory of onP1 and monodromy representations of the braid group. In: Conformal field theory and solvable lattice models. Lett. Math. Phys.13, 303 (1987)Google Scholar
- 10.[KV] Kauffman, L.H., Vogel, P.: Link polynomials and a graphical calculus. Preprint (1987)Google Scholar
- 11.[K] Kirillov, A.N.:q-analog of Clebsch-Gordon coeffcients for slz. Zap. Nauch. Semin. LOMI,170, 1988Google Scholar
- 12.[KR] Kirillov, A.N., Reshetikhin, N.Yu.: Representation of the algebraU q(sl 2),q-orthogonal polynomials and invariants of links. LOMI-preprint, E-9-88, Leningrad 1988Google Scholar
- 13.[L] Luztig, G.: Quantum derformations of certain simple modules over enveloping algebras. M.I.T. Preprint, December 1987Google Scholar
- 14.[Ma] MacLane, S.: Natural associativity and commutavity. Rice Univ. Studies49, 28–46 (1963)Google Scholar
- 15.[MS] Moore, G., Seiberg, N.: Classical and quantum conformal field theory. Commun. Math. Phys.123, 177–254 (1989)Google Scholar
- 16.[Re1] Reshetikhin, N.Yu.: Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links. I. LOMI-preprint E-4-87 (1988), II. LOMI-preprint E-17-87 (1988)Google Scholar
- 17.[Re2] Reshetikhin, N.Yu.: Quasitriangluar Hopfalgebras and invariants of Tangles. Algebra and Anal.1, (1988) (in Russian)Google Scholar
- 18.[RS] Reshetikhin, N.Yu.: Semenov: Tian-Shansky, M.A.: QuantumR-matrices and factorization problem in quatum groups. J. Geom. Phys. v. V (1988)Google Scholar
- 19.[RO] Rosso, M.: Représentations irréductibles de dimension finie duq-analogue de l'algébre enveloppante d'une algèbre de Lie simple. C.R. Acad. Sci. paris.305, Se'rie 1, 587–590 (1987)Google Scholar
- 20.[Tu1] Turaev, V.G.: The Yang-Baxter equation and invariants of links. Invent. Math.92, 527–553 (1988)Google Scholar
- 21.[Tu2] Turaev, V.G.: The Conways and Kauffman modules of the solid torus with an appendix on the operator invariants of tangles. LOMI Preprint E-6-88. Leningrad (1988)Google Scholar
- 22.[Ye] Yetter, D.N.: Category theoretic representations of Knotted graphs in S3, PreprintGoogle Scholar
- 23.[Wi] Witten, E.: Quantum field theory and the Jones polynomial. Commun. Math. Phys. (in press)Google Scholar
Copyright information
© Springer-Verlag 1990