Classification of realizations of Lie algebras of vector fields on circle
Abstract
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 $\mathfrak{sl}(2,\mathbb R)$ 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.
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