Geometry of Lie integrability by quadratures

Autor:	Cariñena, J. F., Falceto, F., Grabowski, J., Rañada, M. F.
Rok vydání:	2014
Předmět:	Mathematical Physics Mathematics - Classical Analysis and ODEs Nonlinear Sciences - Exactly Solvable and Integrable Systems 37J35 34A34 34C15 70H06
Zdroj:	Journal of Physics A. Mathematical and Theoretical 48(21), 2014
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8113/48/21/215206
Popis:	In this paper we extend the Lie theory of integration in two different ways. First we consider a finite dimensional Lie algebra of vector fields and discuss the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a prescribed way. It turns out that the conditions can be expressed in a purely algebraic way. In a second step we generalize the construction to the case in which we substitute the Lie algebra of vector fields by a module (generalized distribution). We obtain much larger class of integrable systems replacing standard concepts of solvable (or nilpotent) Lie algebra with distributional solvability (nilpotency). Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1409.7549 Zobrazit plný text záznamu View this record from Arxiv