On the Automorphisms of a Free Lie Algebra of Rank 3 Over an Integral Domain

Сибирский математический журнал

article

A. A. Alimbaev¹  R. Zh. Nauryzbaev²  U. U. Umirbaev³ 

[1] U. Sultangazin Kostanai State Pedagogical University;L. N. Gumilyov Eurasian National University;Wayne State University

关键词: free Lie algebra;    automorphism;    tame automorphism;    free product;    Euclidean domain;   

DOI  :  10.1134/S0037446620010012

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We prove that the group of tame automorphisms of a free Lie algebra of rank 3 (as well as of a free anticommutative algebra) over an arbitrary integral domain has the structure of an amalgamated free product. We construct an example of a wild automorphism of a free Lie algebra of rank 3 (as well as of a free anticommutative algebra) over an arbitrary Euclidean ring analogous to the Anick automorphism [1] of free associative algebras.

【 授权许可】

CC BY