Supersymmetric Integrable Hamiltonian Systems, Conformal Lie Superalgebras K (1, N = 1, 2, 3), and Their Factorized Semi-Supersymmetric Generalizations.

Autor: Prykarpatski, Anatolij K., Dilnyi, Volodymyr M., Pukach, Petro Ya., Vovk, Myroslava I.
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Zdroj: Symmetry (20738994); Nov2024, Vol. 16 Issue 11, p1441, 24p
Abstrakt: We successively reanalyzed modern Lie-algebraic approaches lying in the background of effective constructions of integrable super-Hamiltonian systems on functional N = 1 , 2 , 3 - supermanifolds, possessing rich supersymmetries and endowed with suitably related compatible Poisson structures. As an application, we describe countable hierarchies of new nonlinear Lax-type integrable N = 2 , 3 -semi-supersymmetric dynamical systems and constructed their central extended superconformal Lie superalgebra K (1 | 3) and its finite-dimensional coadjoint orbits, generated by the related Casimir functionals. Moreover, we generalized these results subject to the suitably factorized super-pseudo-differential Lax-type representations and present the related super-Poisson brackets and compatible suitably factorized Hamiltonian superflows. As an interesting point, we succeeded in the algorithmic construction of integrable super-Hamiltonian factorized systems generated by Casimir invariants of the centrally extended super-pseudo-differential operator Lie superalgebras on the N = 1 , 2 , 3 -supercircle. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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