Nihonkai Mathematical Journal

The automorphism theorem and additive group actions on the affine plane

Shigeru Kuroda

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Abstract

Due to Rentschler, Miyanishi and Kojima, the invariant ring for a $\mathrm{G}_a$-action on the affine plane over an arbitrary field is generated by one coordinate. In this note, we give a new short proof for this result using the automorphism theorem of Jung and van der Kulk.

Note

Partly supported by JSPS KAKENHI Grant Numbers 15K04826, 24340006.

Article information

Source
Nihonkai Math. J., Volume 28, Number 1 (2017), 65-68.

Dates
Received: 14 April 2016
First available in Project Euclid: 7 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1520391684

Mathematical Reviews number (MathSciNet)
MR3771369

Zentralblatt MATH identifier
06881243

Subjects
Primary: 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
Secondary: 13A50: Actions of groups on commutative rings; invariant theory [See also 14L24] 14R20: Group actions on affine varieties [See also 13A50, 14L30]

Keywords
additive group action affine plane polynomial ring polynomial automorphism Jung-van der Kulk theorem Rentschler theorem

Citation

Kuroda, Shigeru. The automorphism theorem and additive group actions on the affine plane. Nihonkai Math. J. 28 (2017), no. 1, 65--68. https://projecteuclid.org/euclid.nihmj/1520391684


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