Symmetry and Integrability of Equations of Mathematical Physics − 2013
Stanislav Spichak
(Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)
Preliminary classification of realizations of two and threedimensional Lie
algebras of vector fields on a circle
Abstract:
Finitedimensional subalgebras of a Lie algebra of smooth vector fields on a circle,
as well as piecewisesmooth global transformations of a circle on itself, are
considered. A canonical form of realizations of two and three dimensional noncommutative
algebra is obtained. It is shown that all other realizations of smooth vector
fields are reduced to this form using global transformations.
