Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links, I

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia

Last update: 30 May 2014

Notes and References

This is a typed copy of the LOMI preprint Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links, I by N.Yu. Reshetikhin.

Recommended for publication by the Scientific Council of Steklov Mathematical Institute, Leningrad Department (LOMI) 6, June, 1987.


[Yan1967] C.N. Yang, Phys. Rev. Lett. 1967, 19, N 23, p. 1312-1314.

[Bax1982] R. Baxter, Exactly solved models in statistical mechanics, Academic press, London, 1982.

[Fad1984] L.D. Faddeev, Integrable models in (1+1)-dimensional quantum field theory, (Lectures in Les Houches, 1982), Elsevier Science Publishers B:V., 1984.

[KSk1982] P.P. Kulish and E.K. Sklyanin, Lecture Notes in Physics, 1982, 151, p.61.

[KRe1980] P.P. Kulish and N.Yu. Reshetikhin, Zap. Nauch. Semin. LOMI, 1980, 101, p.112 (in Russian).

[Skl1982] E. Sklyanin, Func. Anal. and Appl., 1982, 16, N 4, 27-34 (in Russian).

[SklNONE] E. Sklyanin, ibid, 17, 4, 34-48 (in Russian)..

[Skl1985] E. Sklyanin, Usp. Math. Nauk, 1985, 40, N 2, 214 (in Russian).

[Dri1985] V. Drinfeld, DAN SSSR, 1985, 283, N 5, 1060-1064 (in Russian).

[Dri1986-3] V. Drinfeld, Talk at ICM-86, Berceley, 1986.

[Jim1985] M. Jimbo, Lett. Math. Phys., 1985, 10, N 1, p.63-69.

[Jon1986] V.F.R. Jones, Notes on a talk in Atiyah's seminar, November 1986.

[FYL1985] P. Freyd, D. Yetter, W.B.R. Lickorish, K. Millett, A. Ocneanu and J. Hoste, A new polinomial invariant of knots and links, Bull. Amer. Math. 300., 1985, 12, N 2, p.239-246.

[Che1982] I.V. Cherednik, Teor. Math. Phys., 1982, p.315 (in Russian).

[Tur1988] V. Turaev, The Yang-Baxter equation and invariants of links, Invent. Math. 92 (1988), 527–553.

[Jim1986-2] M. Jimbo, Commun. Math. Phys., 1986, 102, N 4, 537-548.

[Kau1986] L.H. Kauffmann, New Invariants in the Theory of knots, preprint, 1986.

[KRS1981] P.P. Kulish, N.Yu. Reshetikhin and E.K. Sklyanin, Lett. Math. Phys., 1981, 5, p.393.

[Abe1980] E. Abe, Hopf algebras, Cambridge Tracts in Math., N 74, Cambridge University Press, Cambridge, New York, 1980.

[KVe1985] S.V. Kerov and A.M. Vershik, Locally semisimple algebras, Kombinatorial theory and K0-functor,, Modern probl. of Math. (ed. R.V. Gamkrelidse), 26, VINITI, Moskow 1985.

[Bou1981] N. Bourbaki, Groupes et algèbres de Lie, Chapt. IV-VI, Masson, Paris (1981).

[Wen1985] H. Wenzl, Representations of Hecke algebras and subfactors, Thesis, Univ. of Pennsylvania (1985).

[Ker1987] S.V. Kerov, Zap. Nauch. Semin. LOMI, 162, 1987 (in Russian).

[Bir1976] J. Birman, Braids, Links and Mapping Class Groups, Ann. of Math. Studies 82, Princeton Universoty Press, Princeton, 1976.

[Jon1987] V.F.R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. Math. 126 (1987), 335-388.

page history