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arXiv · 2001.00382

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

Alibek Alimbaev·Ruslan Nauryzbaev·Ualbai Umirbaev
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Abstract

We prove that the group of tame automorphisms of a free Lie algebra (as well as of a free anticommutative algebra) rank 3 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 (as well as of a free anticommutative algebra) of rank 3 over an arbitrary Euclidean ring analogous to the Anick automorphism for free associative algebras.

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Alibek Alimbaev, Ruslan Nauryzbaev, Ualbai Umirbaev. 2020-01-02. On the automorphisms of a free Lie algebra of rank 3 over an integral domain. https://doi.org/10.1134/s0037446620010012

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