This article is cited in 3 papers

Mathematical logic, algebra and number theory

Linearization of automorphisms and triangulation of derivations of free algebras of rank 2

A. A. Alimbaev^a, A. S. Naurazbekova^b, D. Kh. Kozybaev<sup>b

a</sup> U. Sultangazin Kostanay State Pedagogical University, 118, Tauelsizdik stк., Kostanay, 110000, Kazakhstan
^b L.N. Gumilyov Eurasian National University, 2, Satpaev str., Nur-Sultan, 010008, Kazakhstan

Abstract: We define a class of $\circ$-varieties of algebras and prove that the tame automorphism group of a free algebra of rank two of any $\circ$-variety of algebras over a field admits an amalgamated free product structure. In particular, the automorphism group of a free right-symmetric algebra of rank two admits an amalgamated free product structure. Using this structure, we prove that any locally finite group of automorphisms of this algebra is conjugate to a subgroup of affine or triangular automorphisms. This implies that any reductive group of automorphisms of a two-generated free right-symmetric algebra is linearizable and any locally nilpotent derivation of this algebra is triangulable over a field of characteristic zero. All of these results are true for free commutative and free non-associative algebras of rank two.

Keywords: free right-symmetric algebra, automorphism, free product, linearization, triangulation.

UDC: 512.5

MSC: 17A36

Received December 19, 2018, published August 20, 2019

DOI: 10.33048/semi.2019.16.077

Bibliographic databases:

•