title: The applications of a higher-dimensional Lie algebra and its decomposed subalgebras.
abstract: With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 x 6 matrix Lie algebra smu(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra smu(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras smu(6) and E is used to directly construct integrable couplings.
authors.affiliation: College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, 266510, PR China.
authors.forename: Zhang
authors.initials: Z
authors.lastname: Yu
authors.forename: Yufeng
authors.initials: Y
authors.lastname: Zhang