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Some algebraic structures connected with the Yang-Baxter equation. (English. Russian original) Zbl 0513.58028
Funct. Anal. Appl. 16, 263-270 (1983); translation from Funkts. Anal. Prilozh. 16, No. 4, 27-34 (1982).

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
17B35 Universal enveloping (super)algebras
81S99 General quantum mechanics and problems of quantization
22E70 Applications of Lie groups to the sciences; explicit representations
Full Text: DOI
[1] P. P. Kulish and E. K. Sklyanin, ”Quantum spectral transform method. Recent developments,” Lect. Notes Phys.,151, 61-119 (1982). · Zbl 0734.35071 · doi:10.1007/3-540-11190-5_8
[2] A. G. Izergin and V. E. Korepin, ”Quantum inverse problem method,” Fiz. Elem. Chastits At. Yad.,13, No. 3, 501-541 (1982).
[3] P. P. Kulish and E. K. Sklyanin, ”On the solutions to the Yang?Baxter equation,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,95, 129-160 (1980).
[4] P. P. Kulish, N. Yu. Reshetikhin, and E. K. Sklyanin, ”Yang?Baxter equation and representation theory,” Lett. Math. Phys.,5, No. 5, 393-403 (1981). · Zbl 0502.35074 · doi:10.1007/BF02285311
[5] A. A. Belavin and V. G. Drinfel’d, ”On the solutions to the classical Yang?Baxter equation for simple Lie algebras,” Funkts. Anal. Prilozhen.,16, No. 3, 1-29 (1982). · Zbl 0498.32010 · doi:10.1007/BF01081801
[6] A. A. Belavin, ”Discrete groups and integrability of quantum systems,” Funkts. Anal. Prilozhen.,14, No. 4, 18-26 (1980). · Zbl 0454.22012
[7] I. M. Krichever, ”Baxter’s equations and algebraic geometry,” Funkts. Anal. Prilozhen.,15, No. 2, 22-35 (1981). · Zbl 0475.35072
[8] A. G. Izergin and V. E. Korepin, ”Lattice versions of quantum field theory models in two dimensions,” Nucl. Phys. B.,205, No. 3, 401-413 (1982). · doi:10.1016/0550-3213(82)90365-0
[9] A. G. Izergin and V. E. Korepin, ”A lattice model connected with the nonlinear Schr?dinger equation,” Dokl. Akad. Nauk SSSR,259, No. 1, 76-79 (1981). · Zbl 0941.82507
[10] R. J. Baxter, ”Partition function for the eight?vertex lattice model,” Ann. Phys.,70, No. 1, 193-228 (1972). · Zbl 0236.60070 · doi:10.1016/0003-4916(72)90335-1
[11] E. K. Sklyanin, ”On complete integrability of the Landau?Lifshitz equation,” Preprint LOMI E-3-1979, Leningrad (1979). · Zbl 0449.35089
[12] A. A. Kirillov, Elements of Representation Theory [in Russian], Nauka, Moscow (1978). · Zbl 0415.60087
[13] I. M. Gel’fand, ”The center of the infinitesimal group ring,” Mat. Sb.,26, No. 1, 103-112 (1950).
[14] V. E. Korepin, ”An analysis of the bilinear relation of the six?vertex model,” Dokl. Akad. Nauk SSSR,265, No. 6, 1361-1364 (1982).
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