This article is cited in 2 papers

On the automorphisms of a free lie algebra of rank 3 over an integral domain

A. A. Alimbaev^a, R. Zh. Nauryzbaev^b, U. U. Umirbaev<sup>c

a</sup> Kostanai State Pedagogical Institute
^b Eurasian National University named after L.N. Gumilyov, Nur-Sultan
^c Wayne State University, Detroit, MI

Abstract: 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.

Keywords: free Lie algebra, automorphism, tame automorphism, free product, Euclidean domain.

UDC: 512.55

Received: 04.03.2019
Revised: 24.04.2019
Accepted: 15.05.2019

DOI: 10.33048/smzh.2020.61.101

 English version: Siberian Mathematical Journal, 2020, 61:1, 1–10

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