Supersymmetric Integrable Hamiltonian Systems, Conformal Lie Superalgebras <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">K</mi></mrow></semantics></math></inline-formula>(1, <i>N</i> = 1, 2, 3), and Their Factorized Semi-Supersymmetric Generalizations

Abstract

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.

Keywords

• supersymmetry
• semi-supersymmetry
• supercircle loop diffeomorphism group
• coadjoint action
• Lax integrability
• loop Lie superalgebra