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

被引：0
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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中图分类号：
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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共 33 条
[11]  
Kozybaev D(2004)Automorphisms of a free associative algebra of rank 2. I, II J. Amer. Math. Soc. 17 197-227
[12]  
Makar-Limanov L(1964)Automorphisms and derivations of free Poisson algebras in two variables Proc. Lond. Math. Soc. 14 618-632
[13]  
Umirbaev U(1968)The Freiheitssatz and the automorphisms of free right-symmetric algebras Trans. Amer. Math. Soc. 132 553-562
[14]  
Alimbaev A A(1947)Linearization of automorphisms and triangulation of derivations of free algebras of rank 2 Mat. Sb. 20 239-262
[15]  
Naurazbekova A S(1954)Tame and wild automorphisms of rings of polynomials in three variables Mat. Sb. 34 81-88
[16]  
Kozybaev D K(1953)Subalgebras of free associative algebras Mat. Sb. 33 441-452
[17]  
Shestakov I P(1956)On Schreier varieties of linear algebras Math. Z. 64 195-216
[18]  
Umirbaev U U(1985)Nonassociative free algebras and free products of algebras Math. Notes 37 356-360
[19]  
Cohn P M(1986)Subalgebras of free commutative and free anticommutative algebras Sib. Math. J. 27 136-140
[20]  
Lewin J(1989)Subalgebras of free Lie algebras Sib. Math. J. 30 903-914
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