A kind of infinite-dimensional Novikov algebras and its realizations. (English) Zbl 1359.17003

Chen, Liangyun

Abstr. Appl. Anal. 2013, Article ID 270937, 5 p. (2013).

Summary: We construct a kind of infinite-dimensional Novikov algebras and give its realization by hyperbolic sine functions and hyperbolic cosine functions.

MSC:

17A30

Nonassociative algebras satisfying other identities

References:

[1]	Gel’fand, I. M.; Diki, L. A., Asymptotic properties of the resolvent of Sturm-Liouville equations, and the algebra of Korteweg-de Vries equations, Functional Analysis and Its Applications, 30, 77-113 (1975) · Zbl 0334.58007
[2]	Gel’fand, I. M.; Diki, L. A., A Lie algebra structure in the formal calculus of variations, Functional Analysis and Its Applications, 10, 16-22 (1976) · Zbl 0347.49023
[3]	Gel’fand, I. M.; Dorfman, I. Y., Hamiltonian operators and algebraic structures associated with them, Functional Analysis and Its Applications, 13, 248-262 (1979) · Zbl 0437.58009
[4]	Ma, W. X., Some Hamiltonian operators in infinite-dimensional Hamiltonian systems, Acta Mathematicae Applicatae Sinica, 13, 4, 484-496 (1990) · Zbl 0725.58020
[5]	Ma, W. X., Complexiton solutions to the Korteweg-de Vries equation, Physics Letters A, 301, 1-2, 35-44 (2002) · Zbl 0997.35066 · doi:10.1016/S0375-9601(02)00971-4
[6]	Tu, G. Z.; Ma, W. X., An algebraic approach for extending Hamiltonian operators, Journal of Partial Differential Equations, 5, 1, 43-56 (1992) · Zbl 0751.58016
[7]	Zel’manov, E. I., A class of local translation-invariant Lie algebras, Soviet Mathematics—Doklady, 35, 1, 216-218 (1987) · Zbl 0629.17002
[8]	Osborn, J. M., Simple Novikov algebras with an idempotent, Communications in Algebra, 20, 9, 2729-2753 (1992) · Zbl 0772.17001 · doi:10.1080/00927879208824486
[9]	Osborn, J. M., Infinite-dimensional Novikov algebras of characteristic \(0\), Journal of Algebra, 167, 1, 146-167 (1994) · Zbl 0814.17002 · doi:10.1006/jabr.1994.1181
[10]	Xu, X., Hamiltonian operators and associative algebras with a derivation, Letters in Mathematical Physics, 33, 1, 1-6 (1995) · Zbl 0837.16034 · doi:10.1007/BF00750806
[11]	Xu, X., On simple Novikov algebras and their irreducible modules, Journal of Algebra, 185, 3, 905-934 (1996) · Zbl 0863.17003 · doi:10.1006/jabr.1996.0356
[12]	Xu, X., Novikov-Poisson algebras, Journal of Algebra, 190, 2, 253-279 (1997) · Zbl 0872.17030 · doi:10.1006/jabr.1996.6911
[13]	Xu, X., Variational calculus of supervariables and related algebraic structures, Journal of Algebra, 223, 2, 396-437 (2000) · Zbl 1012.37048 · doi:10.1006/jabr.1999.8064
[14]	Bai, C.; Meng, D., The realization of non-transitive Novikov algebras, Journal of Physics A, 34, 33, 6435-6442 (2001) · Zbl 1003.17002 · doi:10.1088/0305-4470/34/33/308
[15]	Bai, C.; Meng, D., A Lie algebraic approach to Novikov algebras, Journal of Geometry and Physics, 45, 1-2, 218-230 (2003) · Zbl 1033.17001 · doi:10.1016/S0393-0440(02)00150-X
[16]	Bai, C.; Meng, D., On the Novikov algebra structures adapted to the automorphism structure of a Lie group, Journal of Geometry and Physics, 45, 1-2, 105-115 (2003) · Zbl 1033.17002 · doi:10.1016/S0393-0440(02)00127-4
[17]	Chen, L.; Niu, Y.; Meng, D., Two kinds of Novikov algebras and their realizations, Journal of Pure and Applied Algebra, 212, 4, 902-909 (2008) · Zbl 1136.17002 · doi:10.1016/j.jpaa.2007.07.008
[18]	Kang, Y.; Chen, Z., Novikov superalgebras in low dimensions, Journal of Nonlinear Mathematical Physics, 16, 3, 251-257 (2009) · Zbl 1232.17011 · doi:10.1142/S1402925109000212
[19]	Zhu, F.; Chen, Z., Novikov superalgebras with \(A_0 = A_1 A_1\), Czechoslovak Mathematical Journal, 60(135), 4, 903-907 (2010) · Zbl 1224.17010 · doi:10.1007/s10587-010-0076-5