Every monomorphism of the Lie algebra of unitriangular polynomial derivations is an automorphism

2012/05/03 by V. V. Bavula, Bavula, V. V.
Mathematics · Physics and Astronomy · #17B30 #17B40 #17B65 #17B66 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1205.0797

openalex publication_date 2012/05/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that every monomorphism of the Lie algebra \ggu_n of unitriangular derivations of the polynomial algebra P_n=K[x₁,..., x_n] is an automorphism.

Related

• The groups of automorphisms of the Lie algebras of unitriangular polynomial derivations
• The group of automorphisms of the Lie algebra of derivations of a polynomial algebra
• The group of automorphisms of the Lie algebra of derivations of a field of rational functions
• Automorphisms and derivations on algebras endowed with formal infinite sums
• The group of automorphisms of the algebra of one-sided inverses of a polynomial algebra, II