Xu, Xiaoping Hamiltonian operators and associative algebras with a derivation. (English) Zbl 0837.16034 Lett. Math. Phys. 33, No. 1, 1-6 (1995). Summary: We prove that an algebraic structure proposed by I. M. Gel’fand and I. Ya. Dorfman [Funct. Anal. Appl. 13, 248–262 (1980); translation from Funkts. Anal. Prilozh. 13, No. 4, 13–30 (1979; Zbl 0428.58009)] in studying Hamiltonian operators is equivalent to an associative algebra with a derivation under a unitary condition. Cited in 1 ReviewCited in 12 Documents MSC: 16W25 Derivations, actions of Lie algebras 37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Keywords:Hamiltonian operators; associative algebra; derivation; unitary condition Citations:Zbl 0437.58009; Zbl 0428.58009 PDFBibTeX XMLCite \textit{X. Xu}, Lett. Math. Phys. 33, No. 1, 1--6 (1995; Zbl 0837.16034) Full Text: DOI References: [1] Balinskii, A. A. and Novikov, S. P.: English transl.Soviet Math. Dokl. 32, 228-231 (1985). [2] Dolan, L., Goddard, P., and Montague, P.:Nuclear Phys. B338, 529-601 (1990). [3] Gel’fand, I. M. and Dikii, L. A.:Russian Math. Surveys 30(5), 77-113 (1975). · Zbl 0334.58007 [4] Gel’fand, I. M. and Dikii, L. A.:Funct. Anal. Appl. 10, 16-22 (1976). · Zbl 0347.49023 [5] Gel’fand, I. M. and Dorfman, I. Ya.:Funct. Anal. Appl. 13, 248-262 (1979). · Zbl 0437.58009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.