A few expanding Lie algebras of the Lie algebra A(1) and applications

摘要

Based on two foundational subalgebras of the Lie algebra A(1), a few expanding higher-dimensional Lie algebras are presented to generate four integrable couplings of a soliton equation hierarchy. The Hamiltonian structure for one of them is obtained by using the quadratic-form identity. The classification of the Lie algebras is also given. Moreover, a decomposition of one higher-dimensional Lie algebra is demonstrated to produce a q-integrable expanding hierarchy for generalized q-form KdV hierarchy. (c) 2006 Elsevier B.V. All rights reserved.