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We successively analyze 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 super-symmetries and endowed with suitably related compatible Poisson structures. As an application, we describe countable hierarchies of new Lax-type integrable nonlinear \(N=2,3\) -semi-supersymmetric dynamical systems and analyze their central extended superconformal Lie superalgebra \(\mathcal {K}(1|3)\) and its finite-dimensional coadjoint orbits, generated by the related Casimir functionals.

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On the Conformal Lie Superalgebras \(\mathcal {K}(1;N=1;2;3)\) and Related Semi-supersymmetric Integrable Systems

  • 会议论文

  • 发表日期：

    2025年

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  • Anatolij K. Prykarpatski,
  • Oksana Ye. Hentosh,
  • Victor A. Bovdi

摘要

We successively analyze 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 super-symmetries and endowed with suitably related compatible Poisson structures. As an application, we describe countable hierarchies of new Lax-type integrable nonlinear \(N=2,3\) -semi-supersymmetric dynamical systems and analyze their central extended superconformal Lie superalgebra \(\mathcal {K}(1|3)\) and its finite-dimensional coadjoint orbits, generated by the related Casimir functionals.