The GLND generation conjecture

From papers

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

GLNDn(k)=eDDLNDn(k), GLn(k).\operatorname{GLND}_n(k)=\langle e^D\mid D\in\operatorname{LND}_n(k),\ \operatorname{GL}_n(k)\rangle.

GLND generation conjecture.

GAn(k)=GLNDn(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.

Progress summary

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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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