Lie algebras associated with group U(n)

Yu Feng Zhang*, Huang He Dong, Hon Wah TAM

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)


Starting from the subgroups of the group U(n), the corresponding Lie algebras of the Lie algebra A1 are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few expanding Lie algebras are obtained by enlarging matrices. Some of them can be devoted to producing double integrable couplings of the soliton hierarchies of nonlinear evolution equations. Others can be used to generate integrable couplings involving more potential functions. The above Lie algebras ewe classifieed into two types. Only one type can generate the integrable couplings, whose Hamiltonian structure could be obtained by use of the quadratic-form identity. In addition, one condition on searching for integrable couplings is improved such that more useful Lie algebras are enlightened to engender. Then two explicit examples are shown to illustrate the applications of the Lie algebras. Finally, with the help of closed cycling operation relations, another way of producing higher-dimensional Lie algebras is given.

Original languageEnglish
Pages (from-to)215-226
Number of pages12
JournalCommunications in Theoretical Physics
Issue number2
Publication statusPublished - 15 Aug 2007

Scopus Subject Areas

  • Physics and Astronomy (miscellaneous)

User-Defined Keywords

  • Group
  • Integrable couplings
  • Lie algebra


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