Advanced Studies in Pure Mathematics

Amalgamations and automorphism groups

David Wright

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Many types of automorphism groups in algebra have nice structures arising from actions on combinatoric spaces. We recount some examples including Nagao's Theorem, the Jung-Van der Kulk Theorem, and a new structure theorem for the tame subgroup $\text{TA}_3(K)$ of the group $\text{GA}_3(K)$ of polynomial automorphisms of $\mathbb{A}_K^3$, for $K$ a field of characteristic zero. We also ask whether a larger collection of automorphism groups possess a similar kind of structure.

Article information

Algebraic Varieties and Automorphism Groups, K. Masuda, T. Kishimoto, H. Kojima, M. Miyanishi and M. Zaidenberg, eds. (Tokyo: Mathematical Society of Japan, 2017), 465-474

Received: 29 June 2015
Revised: 14 June 2016
First available in Project Euclid: 21 September 2018

Permanent link to this document euclid.aspm/1537498716

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14R20: Group actions on affine varieties [See also 13A50, 14L30] 05E18: Group actions on combinatorial structures
Secondary: 13A50: Actions of groups on commutative rings; invariant theory [See also 14L24]

Polynomial automorphism tame automorphism polynomial ring affine space amalgamated product simplicial complex


Wright, David. Amalgamations and automorphism groups. Algebraic Varieties and Automorphism Groups, 465--474, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07510465.

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