On classification of Lie algebra realizations

2017/03/02 by Daniel Gromada, Severin Pošta, Gromada, Daniel +1
Computer Science · Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Polynomial and algebraic computation #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1703.00808

openalex publication_date 2017/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study realizations of Lie algebras by vector fields. A correspondence between classification of transitive local realizations and classification of subalgebras is generalized to the case of regular local realizations. A reasonable classification problem for general realizations is rigorously formulated and an algorithm for construction of such classification is presented.

Related

• On Lie's classification of subalgebras of vector fields on the plane
• Classification of Realizations of Lie Algebras of Vector Fields on a Circle
• Classification of solvable Lie algebras
• On Lie's classification of nonsolvable subalgebras of vector fields on the plane
• Formalizing a classification theorem for low-dimensional solvable Lie algebras in Lean