The GLIN generation conjecture

Let kk be a field, and let GAn(k)\operatorname{GA}_n(k) be the group of polynomial automorphisms. If char(k)2\operatorname{char}(k)\ne2, let GLINn(k)\operatorname{GLIN}_n(k) be the smallest normal subgroup of GAn(k)\operatorname{GA}_n(k) containing the linearizable polynomial automorphisms.

GLIN generation conjecture. If char(k)2\operatorname{char}(k)\ne2, then

GLINn(k)=GAn(k).\operatorname{GLIN}_n(k)=\operatorname{GA}_n(k).

The paper motivates this by the inclusion of tame automorphisms in GLINn(k)\operatorname{GLIN}_n(k) and the result that the Nagata automorphism belongs to GLINn(C)\operatorname{GLIN}_n(\mathbb{C}). The conjecture is presented as new and no resolution is reported.

Sources & referencesView supporting material

Primary source

Stefan Maubach and Pierre-Marie Poloni, “The Nagata automorphism is shifted linearizable”, arXiv:0804.4870 (2008).

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