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.

中文翻译：

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积分域上一个3阶自由李代数的自同构

我们证明了任意积分域上的 3 阶自由李代数（以及自由反对易代数）的驯服自同构群具有合并自由积的结构。我们在任意欧几里得环上构造了一个 3 阶自由李代数（以及自由反对易代数）的野生自同构的例子，类似于自由结合代数的 Anick 自同构 [1]。