Classification of realizations of Lie algebras of vector fields on circle - Spichak, S. V. (Ukrains’kyi Matematychnyi Zhurnal, 2022)
UDC 517.986.5 The realizations of finite-dimensional Lie algebras of smooth tangent vector fields on circle are described. The ``canonical’’ realizations of two-dimensional noncommutative algebra, as well as the algebra sl(2,R) are constructed. It is shown that any realization of these algebras by smooth vector fields is reduced to one of a ``canonical’’ realization by piecewise-smooth global transformations of circle onto itself. Formulas for calculating the number of non-equivalent realizations are obtained.