Super Lie–Poisson Structures, Their Deformations, and Related New Nonlinear Integrable Super-Hamiltonian Systems
Year: 2025
Type: article
Abstract: Lie-algebraic Poisson structures, related to the superalgebra of super-pseudodifferential operators on the circle over the even component of the Z2-graded Grassmann algebra, have been studied in detail; the corresponding coadjoint orbits, generated by the Casimir invariants, regarding the different superalgebra splittings into the subalgebras, are analyzed. The related Lax-type completely integrable Hamiltonian flows are constructed on suitably defined functional manifolds with respect to the canonical super-Lie–Poisson structures on them. An approach was proposed allowing the extension of the related coadjoint flows by means of the respectively constructed super-evolution flows on the adjoint super-subalgebras, specially deformed by means of super-pseudodifferential operator elements, depending on the generalized eigenfunctions of the corresponding super-linear Lax-type spectral problem. As a consequence, it is stated that all constructed new coadjoint superflows generate on the suitably extended supermanifolds Lax-type integrable Hamiltonian systems. The centrally extended super-Lie-algebraic structures have been analyzed and the related coadjoint orbits described, generated by the corresponding Casimir invariants and coinciding with integrable Hamiltonian systems on suitably defined supermanifolds.
Source: Symmetry
DOI: 10.3390/sym17111925
Authors: Anatolij K. Prykarpatski, Myroslava I. Vovk, Petro Ya. Pukach, Yarema A. Prykarpatskyy
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4416074234