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

被引：0
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作者：
A. A. Alimbaev
R. Zh. Nauryzbaev
U. U. Umirbaev
机构：
[1] U. Sultangazin Kostanai State Pedagogical University,
[2] L. N. Gumilyov Eurasian National University,undefined
[3] Wayne State University,undefined
来源：
Siberian Mathematical Journal | 2020年 / 61卷
关键词：
free Lie algebra; automorphism; tame automorphism; free product; Euclidean domain;
D O I：
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学科分类号：
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.
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页码：1 / 10
页数：9
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