Invertible linear transformations and the Lie algebras

Yufeng Zhang*, Hon Wah TAM, Fukui Guo

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

11 Citations (Scopus)


With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.

Original languageEnglish
Pages (from-to)682-702
Number of pages21
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number4
Publication statusPublished - Jul 2008

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

User-Defined Keywords

  • Invertible linear transformation
  • Lie algebra
  • Soliton hierarchy


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