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 three-dimensional Lie algebras of vector fields on a circle

Finite-dimensional subalgebras of a Lie algebra of smooth vector fields on a circle, as well as piecewise-smooth 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.