Set-theoretical solutions to the quantum yang-baxter equation

Duke Mathematical Journal

Volumn 100, Issue 2, 1999, Pages 169-209

  Etingof, Pavel ^a   Schedler, Travis ^b   Soloviev, Alexandre ^c  

^a HARVARD UNIVERSITY   (United States)

^b 2312 Harvard Yard Mail Center ^*  (Japan)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033570864     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-99-10007-X     Document Type: Article

References (15)

1. V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, 2d ed., Grundlehren Math. Wiss. 250, Springer-Verlag, New York, 1988.
2. M. Aschbacher, Finite Group Theory, Cambridge Stud. Adv. Math. 10, Cambridge Univ. Press, Cambridge, 1993.
3. D. Burde, Affine structures on nilmanifolds, Internat. J. Math. 7 (1996), 599-616.
4. P. Deligne and J. Milne, “Tannakian categories” in Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Math. 900, Springer-Verlag, Berlin, 1982, 101-228.
5. V. G. Drinfeld, “On some unsolved problems in quantum group theory” in Quantum Groups (Leningrad, 1990), Lecture Notes in Math. 1510, Springer-Verlag, Berlin, 1992, 1-8.
6. P. Etingof and S. Gelaki, A method of construction of finite-dimensional triangular semisimple Hofp algebras, Math. Res. Lett. 5 (1998), 551-561.
7. T. Gateva-Ivanova and M. Van den Bergh, Semigroups of I-type, J. Algebra 206 (1998), 97-112.
8. T. Hayashi, Quantum groups and quantum semigroups, J. Algebra 204 (1998), 225-254.
9. J. Hietarinta, Permutation-type solutions to the Yang-Baxter and other n-simplex equations, J. Phys. A 30 (1997), 4757-4771.
10. J.-H. Lu, M. Yan, and Y.-C. Zhu, Positive Hopf algebra and set-theoretical Yang-Baxter equation, to appear.
11. N. Yu. Reshetikhin, L. A. Takhtadzhyan, and L. D. Faddeev, Quantization of Lie groups and Lie algebras (in Russian), Algebra i Analiz 1 (1989), 178-206;
12. N. Yu. Reshetikhin, L. A. Takhtadzhyan, and L. D. Faddeev, Quantization of Lie groups and Lie algebras (in Russian), Leningrad Math. J. 1 (1990), 193-225.
13. P. Schauenburg, Tannaka Duality for Arbitrary Hopf Algebras, Algebra Ber. 66, Fischer, Munich, 1992.
14. V. Turaev, Quantum Invariants of Knots and 3-Manifolds, de Gruyter Stud. Math. 18, de Gruyter, Berlin, 1994.
15. A. Weinstein and P. Xu, Classical solutions of the quantum Yang-Baxter equation, Comm. Math. Phys. 148 (1992), 309-343.