Deforming lie algebras to frobenius integrable nonautonomous hamiltonian systems
نویسندگان
چکیده
Motivated by the theory of Painlev\'e equations and associated hierarchies, we study non-autonomous Hamiltonian systems that are Frobenius integrable. We establish sufficient conditions under which a given finite-dimensional Lie algebra vector fields can be deformed to time-dependent integrable spanning same distribution as original algebra. The results applied quasi-St\"ackel systems.
منابع مشابه
g-QUASI-FROBENIUS LIE ALGEBRAS
A Lie version of Turaev’s G-Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a g-quasi-Frobenius Lie algebra for g a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra (q, β) together with a left g-module structure which acts on q via derivations and for which β is g-inva...
متن کاملIntegrable Hamiltonian systems on Lie groups : Kowalewski type
The contributions of Sophya Kowalewski to the integrability theory of the equations for the heavy top extend to a larger class of Hamiltonian systems on Lie groups; this paper explains these extensions, and along the way reveals further geometric significance of her work in the theory of elliptic curves. Specifically, in this paper we shall be concerned with the solutions of the following diffe...
متن کاملTableaux over Lie algebras, integrable systems and classical surface theory
Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, and other classical soliton surfaces. Completely integrable equations such as the G/G0-system of Terng...
متن کاملSymmetric Designs on Lie Algebras and Interactions of Hamiltonian Systems
Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of symmetric designs on Lie algebras. The results of analysis of these equations show that some class of symmetric designs on Lie algebras beyond Jordan ones may be useful for a description of almost periodic, asymptotically periodic, almost asymptotically periodic, and possibly, more cha...
متن کاملq-Deforming Maps for Lie Group Covariant Heisenberg Algebras
We briefly summarize our systematic construction procedure of qdeforming maps for Lie group covariant Weyl or Clifford algebras. Talk presented at the Fifth Wigner Symposium, 25-29 August 1997, Vienna, Germany. Submitted for the proceedings of the Conference.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Reports on Mathematical Physics
سال: 2021
ISSN: ['0034-4877', '1879-0674']
DOI: https://doi.org/10.1016/s0034-4877(21)00028-8