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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

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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)

Information

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. 

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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