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Variational calculus of supervariables and related algebraic structures. (English) Zbl 1012.37048
The author establishes a formal variational calculus of supervariables, which is a combination of the bosonic theory of Gel’fand-Dikii and the fermionic theory in his earlier work [J. Phys. A, Math. Gen. 28, No. 6, 1681-1698 (1995; Zbl 0852.58043)]. In terms of his theory he finds certain interesting new algebraic structures in connection with Hamiltonian superoperators. In particular, he finds connections between Hamiltonian superoperators and the Novikov-Poisson algebras that he introduced in [J. Algebra 185, No. 3, 905-934 (1996; Zbl 0863.17003)] in order to establish a tensor theory of Novikov algebras. He also proves that an odd linear Hamiltonian superoperator in his variational calculus induces a Lie superalgebra, which is a natural generalization of the super-Virasoro algebra under certain conditions.

MSC:
37K05Hamiltonian structures, symmetries, variational principles, conservation laws
37K30Relations of infinite-dimensional systems with algebraic structures
17B80Applications of Lie algebras to integrable systems
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References:
[1] Balinskii, A. A.; Novikov, S. P.: Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras. Soviet math. Dokl. 32, 228-231 (1985) · Zbl 0606.58018
[2] Dolan, L.; Goddard, P.; Montague, P.: Conformal field theory of twisted vertex operators. Nuclear phys. B 338, 529-601 (1990) · Zbl 0745.17011
[3] Daletsky, Yu.L.: Lie superalgebras in Hamiltonian operator theory. (1984)
[4] Daletsky, Yu.L.: Hamiltonian operators in graded formal calculus of variables. Funct. anal. Appl. 20, 136-138 (1986)
[5] Dewitt, B.: Supermanifolds. (1992) · Zbl 0874.53055
[6] Feingold, A. J.; Frenkel, I. B.; Ries, J. F.: Spinor construction of vertex operator algebras, triality and $E(1)$8. Contemp. math. 121 (1991) · Zbl 0743.17029
[7] Frenkel, I. B.; Lepowsky, J.; Meurman, A.: Vertex operator algebras and the monster. Pure and applied mathematics (1988) · Zbl 0674.17001
[8] Gel’fand, I. M.; Dikii, L. A.: Asymptotic behavior of the resolvent of Sturm--Liouville equations and the algebra of the Korteweg--de Vries equations. Russian math. Surveys 30, 77-113 (1975) · Zbl 0334.58007
[9] Gel’fand, I. M.; Dikii, L. A.: A Lie algebra structure in a formal variational calculation. Funct. anal. Appl. 10, 16-22 (1976) · Zbl 0347.49023
[10] Gel’fand, I. M.; Dorfman, I. Ya.: Hamiltonian operators and algebraic structures related to them. Funct. anal. Appl. 13, 248-262 (1979)
[11] Mathieu, P.: Supersymmetry extension of the Korteweg--de Vries equation. J. math. Phys. 29, 2499-2507 (1988) · Zbl 0665.35076
[12] Negele, J. W.; Orland, H.: Quantum many-particle systems. (1988) · Zbl 0984.82503
[13] Osborn, J. M.: Novikov algebras. Nova J. Algebra geom. 1, 1-14 (1992) · Zbl 0876.17005
[14] Osborn, J. M.: Simple Novikov algebras with an idempotent. Comm. algebra 20, 2729-2753 (1992) · Zbl 0772.17001
[15] Osborn, J. M.: Infinite dimensional Novikov algebras of characteristic 0. J. algebra 167, 146-167 (1994) · Zbl 0814.17002
[16] J. M. Osborn, Modules for Novikov algebras, in, Proceedings of the II International Congress on Algebra, Barnaul, 1991. · Zbl 0842.17002
[17] J. M. Osborn, Modules for Novikov algebras of characteristic 0, preprint. · Zbl 0846.17002
[18] Tsukada, H.: Vertex operator superalgebras. Comm. math. Phys. 18, 2249-2274 (1990) · Zbl 0704.17001
[19] X. Xu, On spinor vertex operator algebras and their modules, J. Algebra191, 427--460. · Zbl 0883.17027
[20] Xu, X.: Hamiltonian operators and associative algebras with a derivation. Lett. math. Phys. 33, 1-6 (1995) · Zbl 0837.16034
[21] Xu, X.: Hamiltonian superoperators. J. phys. A 28, 1681-1698 (1995) · Zbl 0852.58043
[22] Xu, X.: On simple Novikov algebras and their irreducible modules. J. algebra 185, 905-934 (1996) · Zbl 0863.17003
[23] Xu, X.: Novikov--Poisson algebras. J. algebra 190, 253-279 (1997) · Zbl 0872.17030
[24] Xu, X.: Skew-symmetric differential operators and combinatorial identities. Mh. math. 127, 243-258 (1999) · Zbl 0924.05002
[25] Zel’manov, E. I.: On a class of local translation invariant Lie algebras. Soviet math. Dokl. 35, 216-218 (1987)