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The Schouten bracket and Hamiltonian operators. (English) Zbl 0455.58013

Translation from Funkts. Anal. Prilozh. 14, No. 3, 71–74 (1980; Zbl 0444.58010).

MSC:

37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
53D50 Geometric quantization
58J99 Partial differential equations on manifolds; differential operators
58J45 Hyperbolic equations on manifolds
17B80 Applications of Lie algebras and superalgebras to integrable systems

Citations:

Zbl 0444.58010
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References:

[1] I. M. Gel’fand and L. A. Dikii, Usp. Mat. Nauk,30, No. 5, 67-100 (1975).
[2] I. M. Gel’fand and L. A. Dikii, Funkts. Anal. Prilozhen.,10, No. 1, 18-25 (1976).
[3] I. M. Gel’fand and I. Ya. Dorfman, Funkts. Anal. Prilozhen.,13, No. 4, 13-30 (1979).
[4] A. P. Stone, Can. J. Math.,25, No. 5, 903-907 (1973). · Zbl 0261.58001
[5] Yu. I. Manin, Sovrem. Probl. Mat.,11, 5-152 (1978).
[6] I. M. Gel’fand and L. A. Dikii, Funkts. Anal. Prilozhen.,10, No. 4, 13-29 (1976).
[7] M. Adler, ”On a trace functional for formal pseudodifferential operators and the symplectic structure of the Korteweg?de Vries equation,” Preprint (1979). · Zbl 0495.35072
[8] I. M. Gel’fand and L. A. Dikii, ”The family of Hamiltonian structures connected with integrable nonlinear equations,” Preprint Inst. Prikl. Mat. Akad. Nauk SSSR, No. 136 (1978).
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