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

Jian Zhou () and Shiyin Zhao
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Jian Zhou: School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
Shiyin Zhao: School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China

Mathematics, 2024, vol. 12, issue 21, 1-13

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.

Keywords: vector-product Lie algebra; integrable hierarchy; vector-product identity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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