Rips's tame-generation conjecture in positive characteristic

Let KK be an infinite base field with characteristic p2p\neq 2, and let n>3n>3. Consider the polynomial ring K[x1,,xn]K[x_1,\ldots,x_n] and the automorphism

ψ:x1x1+x2x3,x2x2,,xnxn.\psi: x_1\mapsto x_1+x_2x_3,\qquad x_2\mapsto x_2,\qquad\ldots,\qquad x_n\mapsto x_n.

Rips's conjecture. Linear automorphisms, together with ψ\psi, generate the entire tame automorphism group of K[x1,,xn]K[x_1,\ldots,x_n]. The characteristic-zero analogue is known, while the positive-characteristic case has a subtle gap in the existing proof and remains open.

Sources & referencesView supporting material

Primary source

Alexei Belov-Kanel, Andrey Elishev and Jie-Tai Yu, “On Automorphisms of the Tame Polynomial Automorphism Group in Positive Characteristic”, arXiv:2103.12784 (2021).

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