In this paper, the authors define the center of a Symplectic ternary algebra, and investigate the relationship between the center of a Symplectic ternary algebra and that of the Lie triple system associated with it. A...In this paper, the authors define the center of a Symplectic ternary algebra, and investigate the relationship between the center of a Symplectic ternary algebra and that of the Lie triple system associated with it. As an application of the relationship, the unique decomposition theorem for Symplectic ternary algebras with trivial center is obtained.展开更多
Let F be a field with char F = 2, l a maximal nilpotent subalgebra of the symplectic algebra sp（2m,F）. In this paper, we characterize linear maps of l which preserve zero Lie brackets in both directions. It is shown...Let F be a field with char F = 2, l a maximal nilpotent subalgebra of the symplectic algebra sp（2m,F）. In this paper, we characterize linear maps of l which preserve zero Lie brackets in both directions. It is shown that for m ≥ 4, a map φ of l preserves zero Lie brackets in both directions if and only if φ = ψcσT0λαφdηf, where ψc,σT0,λα,φd,ηf are the standard maps preserving zero Lie brackets in both directions.展开更多
The purpose of this paper is to explore an extension of some fundamental properties of the Hamiltonian systems to a more general case. We first extend symplectic group to a general N- group, GN, and prove that it has...The purpose of this paper is to explore an extension of some fundamental properties of the Hamiltonian systems to a more general case. We first extend symplectic group to a general N- group, GN, and prove that it has certain similar properties. A particular property of GN is that as a Lie group dim (GN)≥1. Certain properties of its Lie-algebra 9N are investigated. The results obtained are used to investigate the structure-preserving systems, which generalize the property of symplectic form preserving of Hamiltonian system to a covariant tensor field preserving of certain dynamic systems. The results provide a theoretical benchmark of applying symplectic algorithm to a considerably larger class of structure-preserving systems.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 10871192)
文摘In this paper, the authors define the center of a Symplectic ternary algebra, and investigate the relationship between the center of a Symplectic ternary algebra and that of the Lie triple system associated with it. As an application of the relationship, the unique decomposition theorem for Symplectic ternary algebras with trivial center is obtained.
基金Supported by the Doctor Foundation of Henan Polytechnic University (Grant No.B2010-93)the Natural Science Research Program of Education Department of Henan Province (Grant No.2011B110016)+1 种基金the Natural Science Foundation of Henan Province (Grant No. 112300410120)Applied Mathematics Provincial-level Key Discipline of Henan Province
文摘Let F be a field with char F = 2, l a maximal nilpotent subalgebra of the symplectic algebra sp（2m,F）. In this paper, we characterize linear maps of l which preserve zero Lie brackets in both directions. It is shown that for m ≥ 4, a map φ of l preserves zero Lie brackets in both directions if and only if φ = ψcσT0λαφdηf, where ψc,σT0,λα,φd,ηf are the standard maps preserving zero Lie brackets in both directions.
基金National Natural Science Foundation of China (No.G59837270, G1998020308) and the National Key Project of China.
文摘The purpose of this paper is to explore an extension of some fundamental properties of the Hamiltonian systems to a more general case. We first extend symplectic group to a general N- group, GN, and prove that it has certain similar properties. A particular property of GN is that as a Lie group dim (GN)≥1. Certain properties of its Lie-algebra 9N are investigated. The results obtained are used to investigate the structure-preserving systems, which generalize the property of symplectic form preserving of Hamiltonian system to a covariant tensor field preserving of certain dynamic systems. The results provide a theoretical benchmark of applying symplectic algorithm to a considerably larger class of structure-preserving systems.
