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The applications of a higher-dimensional Lie algebra and its decomposed subalgebras

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  • Yu, Zhang
  • Zhang, Yufeng

Abstract

With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6×6 matrix Lie algebra sμ(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 sμ(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras sμ(6) and E is used to directly construct integrable couplings.

Suggested Citation

  • Yu, Zhang & Zhang, Yufeng, 2009. "The applications of a higher-dimensional Lie algebra and its decomposed subalgebras," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 399-406.
  • Handle: RePEc:eee:chsofr:v:39:y:2009:i:1:p:399-406
    DOI: 10.1016/j.chaos.2007.04.011
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