The Anick automorphism of free associative algebras
Ualbai Umirbaev
TL;DR
This paper proves that the Anick automorphism of a free associative algebra over a field of characteristic zero is a wild automorphism, highlighting its complex and non-tame nature.
Contribution
It establishes the wildness of the Anick automorphism, a significant result in the study of automorphisms of free associative algebras.
Findings
The Anick automorphism is proven to be wild.
The result applies to free associative algebras over any field of characteristic zero.
It advances understanding of automorphism complexity in algebraic structures.
Abstract
We prove that the well-known Anick automorphism of the free associative algebra F<x,y,z> over an arbitrary field F of characteristic 0 is wild.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Differential Equations and Dynamical Systems · Algebraic structures and combinatorial models