The GLND generation conjecture

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Let kk be a field of characteristic zero. Let GA⁡n(k)\operatorname{GA}_n(k) be the group of polynomial automorphisms, let LND⁡n(k)\operatorname{LND}_n(k) denote the locally nilpotent derivations, and define

GLND⁡n(k)=⟨eD∣D∈LND⁡n(k), GL⁡n(k)⟩.\operatorname{GLND}_n(k)=\langle e^D\mid D\in\operatorname{LND}_n(k),\ \operatorname{GL}_n(k)\rangle.

GLND generation conjecture.

GA⁡n(k)=GLND⁡n(k).\operatorname{GA}_n(k)=\operatorname{GLND}_n(k).

This is one of several proposed generation conjectures for polynomial automorphism groups by more understandable classes of automorphisms. Its status is not resolved in the supplied text.

References

Primary source

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

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