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THE FACTORIAL CONJECTURE AND IMAGES OF LOCALLY NILPOTENT DERIVATIONS

Part of: Differential algebra Affine geometry

Published online by Cambridge University Press:  20 May 2019

DAYAN LIU  and
XIAOSONG SUN Open the ORCID record for XIAOSONG SUN [Opens in a new window]
DAYAN LIU
Affiliation:
School of Mathematics, Jilin University, Changchun, 130012, China email liudayan@jlu.edu.cn
XIAOSONG SUN*
Affiliation:
School of Mathematics, Jilin University, Changchun, 130012, China email sunxs@jlu.edu.cn
*
✉sunxs@jlu.edu.cn
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Abstract

The factorial conjecture was proposed by van den Essen et al. [‘On the image conjecture’, J. Algebra 340(1) (2011), 211–224] to study the image conjecture, which arose from the Jacobian conjecture. We show that the factorial conjecture holds for all homogeneous polynomials in two variables. We also give a variation of the result and use it to show that the image of any linear locally nilpotent derivation of $\mathbb{C}[x,y,z]$ is a Mathieu–Zhao subspace.

Keywords

factorial conjectureJacobian conjecturelocally nilpotent derivationsMathieu–Zhao subspaces

MSC classification

Primary: 14R15: Jacobian problem
Secondary: 13N15: Derivations 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 1 , February 2020 , pp. 71 - 79
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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Footnotes

This work was supported by the NSF of China (grants 11871241 and 11771176), the EDJP of China (JJKH20190185KJ) and the China Scholarship Council.

References

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