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A Vector-Product Lie Algebra of a Reductive Homogeneous Space and Its Applications

Author

Listed:
  • Jian Zhou

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
    School of Mathematical, Suqian University, Suqian 223800, China)

  • Shiyin Zhao

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
    School of Mathematical, Suqian University, Suqian 223800, China)

Abstract

A new vector-product Lie algebra is constructed for a reductive homogeneous space, which can lead to the presentation of two corresponding loop algebras. As a result, two integrable hierarchies of evolution equations are derived from a new form of zero-curvature equation. These hierarchies can be reduced to the heat equation, a special diffusion equation, a general linear Schrödinger equation, and a nonlinear Schrödinger-type equation. Notably, one of them exhibits a pseudo-Hamiltonian structure, which is derived from a new vector-product identity proposed in this paper.

Suggested Citation

  • Jian Zhou & Shiyin Zhao, 2024. "A Vector-Product Lie Algebra of a Reductive Homogeneous Space and Its Applications," Mathematics, MDPI, vol. 12(21), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3322-:d:1504916
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