Literature Cited
A. A. Belavin, "Discrete groups and integrability of quantum systems," Funkts. Anal.,14, No. 4, 18–26 (1980).
A. V. Zhiber and A. B. Shabat, "Klein—Gordon equations with nontrivial group," Dokl. Akad. Nauk SSSR,247, No. 5, 1103–1107 (1979).
V. G. Kats, "Automorphisms of finite order of semisimple Lie algebras," Funkts. Anal. Anal.,3, No. 3, 94–96 (1969).
V. G. Kats, "Simple irreducible graded Lie algebras of finite height," Izv. Akad. Nauk SSSR, Ser. Mat.,32, No. 6, 1323–1367 (1968).
P. P. Kulish and E. K. Sklyanin, "Solutions of the Yang—Baxter equation," in: Differential Geometry of Lie Groups and Mechanics [in Russian], Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,95, 129–160 (1980).
A. N. Leznov, M. V. Savel'ev, and V. G. Smirnov, "Theory of representations of groups and integration of nonlinear dynamical systems," Preprint IFVE, 80-51, Serpukhov: IFVE (1980).
I. G. MacDonald, "Affine systems of roots and the Dedekindŋ-function," Matematika,16, No. 4, 3–49 (1972).
J.-P. Serre, Lie Algebras and Lie Groups, W. A. Benjamin (1965).
I. V. Cherednik, "Method of construction of factorized S-matrices in elementary functions," Teor. Mat. Fiz.,43, No. 1, 117–119 (1980).
O. I. Bogoyavlensky, "On perturbations of the periodic Toda lattice," Commun. Math. Phys.,51, 201–209 (1976).
V. G. Kac, "Infinite-dimensional algebras, Dedekind'sŋ-function, classical Möbius function and the very strange formula," Adv. Math.,30, No. 2, 85–136 (1978).
A. V. Michailov, M. A. Olshanetsky, and A. M. Perelomov, Preprint ITEP-64, Moscow: ITEP (1980).
S. A. Bulgadaev, "Two-dimensional integrable field theories connected with simple Lie algebras," P. L., 96B, 151–153 (1980).
A. I. Ooms, "On Lie algebras having a primitive universal enveloping algebra," J. Algebra,32, No. 3, 488–500 (1975).
A. I. Ooms, "On Lie algebras with primitive envelopes — Supplements," Proc. Am. Math. Soc.,58, 67–72 (1976).
A. I. Ooms, "On Frobenius Lie algebras," Commun. Algebra, 8(1), 13–52 (1980).
A. Weil, Varietes Abeliennes et Courbes Algebriques, Hermann, Paris (1948).
A. Weil, "On algebraic groups of transformations," Am. J. Math.,77, 355–391 (1955).
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L. D. Landau Institute of Theoretical Physics, Academy of Sciences of the USSR. Physicotechnical Institute of Low Temperatures, Academy of Sciences of the Ukrainian SSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 16, No. 3, pp. 1–29, July–September, 1982.
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Belavin, A.A., Drinfel'd, V.G. Solutions of the classical Yang - Baxter equation for simple Lie algebras. Funct Anal Its Appl 16, 159–180 (1982). https://doi.org/10.1007/BF01081585
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DOI: https://doi.org/10.1007/BF01081585