Deforming lie algebras to frobenius integrable nonautonomous hamiltonian systems

@article{54461,
   author = {Sergyeyev, Artur and Błaszak, Maciej and Marciniak, Krzysztof},
   article_location = {Oxford (GB)},
   article_number = {2},
   doi = {http://dx.doi.org/10.1016/S0034-4877(21)00028-8},
   keywords = {Frobenius integrability; Lie algebras; Liouville integrability; quasi-Stäckel systems; separable systems},
   language = {eng},
   issn = {0034-4877},
   journal = {Reports on Mathematical Physics},
   title = {Deforming lie algebras to frobenius integrable nonautonomous hamiltonian systems},
   url = {https://www.sciencedirect.com/science/article/pii/S0034487721000288},
   volume = {87},
   year = {2021}
}

TY  - JOUR
ID  - 54461
AU  - Sergyeyev, Artur - Błaszak, Maciej - Marciniak, Krzysztof
PY  - 2021
TI  - Deforming lie algebras to frobenius integrable nonautonomous hamiltonian systems
JF  - Reports on Mathematical Physics
VL  - 87
IS  - 2
SP  - 249-263
EP  - 249-263
PB  - Elsevier Ltd.
SN  - 00344877
KW  - Frobenius integrability
KW  - Lie algebras
KW  - Liouville integrability
KW  - quasi-Stäckel systems
KW  - separable systems
UR  - https://www.sciencedirect.com/science/article/pii/S0034487721000288
N2  - Motivated by the theory of Painlevé equations and associated hierarchies, we study nonautonomous Hamiltonian systems that are Frobenius integrable. We establish sufficient conditions under which a given finite-dimensional Lie algebra of Hamiltonian vector fields can be deformed into a time-dependent Lie algebra of Frobenius integrable vector fields spanning the same distribution as the original algebra. The results are applied to quasi-Stäckel systems from [14].
ER  - 

SERGYEYEV, Artur, Maciej BŁASZAK and Krzysztof MARCINIAK. Deforming lie algebras to frobenius integrable nonautonomous hamiltonian systems. \textit{Reports on Mathematical Physics}. Oxford (GB): Elsevier Ltd., 2021, vol.~87, No~2, p.~249-263. ISSN~0034-4877. Available from: https://dx.doi.org/10.1016/S0034-4877(21)00028-8.