PreprintCC BY-NC-SA 4.0arXiv
An explicit tame factorization of the four-variable Anick automorphism
Abstract
Let δ=xz−yt. We give an explicit tame factorization of the Anick automorphism (x+δt,y+δz,z,t) of $F[x,y,z,t]$. After a linear change of coordinates, the factorization consists of sixteen elementary automorphisms, all fixing z. The proof uses a commutator construction with variables already present in the algebra. A complete list of the elementary factors is included in Section 5. The explicit polynomial factorization identities are defined over ZZ[1/2]; no conclusion in characteristic $2$ is asserted.
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BibTeX
@misc{miasnikov2026explicit,
title = {{An explicit tame factorization of the four-variable Anick automorphism}},
author = {Alexei Miasnikov and Ivan Shestakov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11013},
eprint = {2610.11013},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11013},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - An explicit tame factorization of the four-variable Anick automorphism
AU - Alexei Miasnikov
AU - Ivan Shestakov
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.11013
UR - https://arxiv.org/abs/2610.11013
AB - Let δ=xz−yt. We give an explicit tame factorization of the Anick automorphism (x+δt,y+δz,z,t) of $F[x,y,z,t]$. After a linear change of coordinates, the factorization consists of sixteen elementary automorphisms, all fixing z. The proof uses a commutator construction with variables already present in the algebra. A complete list of the elementary factors is included in Section 5. The explicit polynomial factorization identities are defined over ZZ[1/2]; no conclusion in characteristic $2$ is asserted.
ER -