Classification of Realizations of Lie Algebras of Vector Fields on a Circle

2013/04/08 by Stanislav Spichak, Spichak, Stanislav
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1304.2241

openalex publication_date 2013/04/08 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

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 forms of realizations of two- and three-dimensional noncommutative algebras are obtained. It is shown that all other realizations of smooth vector fields are reduced to this form using global transformations. Some combinatorial formulas for the number of inequivalent realizations of these algebras are obtained.

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