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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 1, Pages 3–16
DOI: https://doi.org/10.33048/smzh.2020.61.101 (Mi smj5961) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

A. A. Alimbaeva, R. Zh. Nauryzbaevb, U. U. Umirbaevc

a Kostanai State Pedagogical Institute
b Eurasian National University named after L.N. Gumilyov, Nur-Sultan
c Wayne State University, Detroit, MI
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DOI: https://doi.org/10.33048/smzh.2020.61.101
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.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan АР05133009
The authors were partially supported under Project AP05133009 by the Institute of Mathematics and Mathematical Modeling of the Ministry of Education and Science of the Republic of Kazakhstan.
Received: 04.03.2019
Revised: 24.04.2019
Accepted: 15.05.2019
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 1, Pages 1–10
DOI: https://doi.org/10.1134/S0037446620010012
Bibliographic databases:
Document Type: Article
UDC: 512.55
Language: Russian
Citation: A. A. Alimbaev, R. Zh. Nauryzbaev, U. U. Umirbaev, “On the automorphisms of a free lie algebra of rank 3 over an integral domain”, Sibirsk. Mat. Zh., 61:1 (2020), 3–16; Siberian Math. J., 61:1 (2020), 1–10
Citation in format AMSBIB
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\paper On the automorphisms of a~free lie algebra of rank~ 3 over an~integral domain
\jour Sibirsk. Mat. Zh.
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\vol 61
\issue 1
\pages 3--16
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\crossref{https://doi.org/10.33048/smzh.2020.61.101}
\transl
\jour Siberian Math. J.
\yr 2020
\vol 61
\issue 1
\pages 1--10
\crossref{https://doi.org/10.1134/S0037446620010012}
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    • This publication is cited in the following 1 articles:
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    		Сибирский математический журнал Siberian Mathematical Journal
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