Geometry of Lie integrability by quadratures
Autor: | Cariñena, J. F., Falceto, F., Grabowski, J., Rañada, M. F. |
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Rok vydání: | 2014 |
Předmět: | |
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 |
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