A subalgebra of Lie algebra A(2) and its associated two types of loop algebras, as well as Hamiltonian structures of integrable hierarchy

作者：Dong Huan he^*

来源：Journal of Mathematical Physics, 2009, 50(5): 053519.

DOI：10.1063/1.3122667

• classical mechanics
• Lie algebras
• matrix algebra

In this paper, a subalgebra A(2) of the Lie algebra A(2) is constructed, which gives a corresponding loop algebra A(2) by properly choosing the gradation of the basis elements. It follows that an isospectral problem is established and a new Liouville integrable Hamiltonian hierarchy is obtained. By making use of a matrix transformation, a subalgebra A(2) of the Lie algebra A(1) is presented, which possesses the same communicative operations of basis elements as those in A(2). Again we expand the Lie algebra A(1) into a high-dimensional loop algebra G, and a type of expanding integrable system of the hierarchy obtained above is worked out. Furthermore, Hamiltonian structures of hierarchy are presented by use of the quadratic form identity.

• 出版日期2009-5
• 单位山东科技大学