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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 1133–1146 (Mi semr1118)  

Mathematical logic, algebra and number theory

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

A. A. Alimbaeva, A. S. Naurazbekovab, D. Kh. Kozybaevb

a U. Sultangazin Kostanay State Pedagogical University, 118, Tauelsizdik st., 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.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan 05133009


DOI: https://doi.org/10.33048/semi.2019.16.077

Full text: PDF file (188 kB)
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Bibliographic databases:

UDC: 512.5
MSC: 17A36
Received December 19, 2018, published August 20, 2019

Citation: A. A. Alimbaev, A. S. Naurazbekova, D. Kh. Kozybaev, “Linearization of automorphisms and triangulation of derivations of free algebras of rank 2”, Sib. Èlektron. Mat. Izv., 16 (2019), 1133–1146

Citation in format AMSBIB
\Bibitem{AliNauKoz19}
\by A.~A.~Alimbaev, A.~S.~Naurazbekova, D.~Kh.~Kozybaev
\paper Linearization of automorphisms and triangulation of derivations of free algebras of rank 2
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1133--1146
\mathnet{http://mi.mathnet.ru/semr1118}
\crossref{https://doi.org/10.33048/semi.2019.16.077}


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