The affine automorphism group of A^3 is not a maximal subgroup of the tame automorphism group

@article{Edo2014TheAA,
  title={The affine automorphism group of A^3 is not a maximal subgroup of the tame automorphism group},
  author={Eric Edo and Drew Lewis},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
  • E. EdoD. Lewis
  • Published 3 October 2014
  • Mathematics
  • arXiv: Algebraic Geometry
We construct explicitly a family of proper subgroups of the tame automorphism group of affine three-space (in any characteristic) which are generated by the affine subgroup and a non-affine tame automorphism. One important corollary is the titular result that settles negatively the open question (in characteristic zero) of whether the affine subgroup is a maximal subgroup of the tame automorphism group. We also prove that all groups of this family have the structure of an amalgamated free… 

Figures from this paper

NORMAL SUBGROUPS GENERATED BY A SINGLE POLYNOMIAL AUTOMORPHISM

  • D. Lewis
  • Mathematics
    Transformation Groups
  • 2019
We study criteria for deciding when the normal subgroup generated by a single special polynomial automorphism of 𝔸n is as large as possible, namely, equal to the normal closure of the special linear

NORMAL SUBGROUPS GENERATED BY A SINGLE POLYNOMIAL AUTOMORPHISM

  • D. Lewis
  • Mathematics
    Transformation Groups
  • 2019
We study criteria for deciding when the normal subgroup generated by a single special polynomial automorphism of 𝔸 n is as large as possible, namely, equal to the normal closure of the special

A non-tame and non-co-tame automorphism of the polynomial ring

An automorphism $F$ of the polynomial ring in $n$ variables over a field of characteristic zero is said to be {\it co-tame} if the subgroup of the automorphism group of the polynomial ring generated

A new co-tame automorphism of the polynomial ring

In this paper, we discuss subgroups of the automorphism group of the polynomial ring in n variables over a field of characteristic zero. An automorphism F is said to be {\it co-tame} if the subgroup

STABLY CO-TAME POLYNOMIAL AUTOMORPHISMS OVER COMMUTATIVE RINGS

We say that a polynomial automorphism ϕ in n variables is stably co-tame if the tame subgroup in n variables is contained in the subgroup generated by ϕ and affine automorphisms in n+1 variables. In

STABLY CO-TAME POLYNOMIAL AUTOMORPHISMS OVER COMMUTATIVE RINGS

  • S. Kuroda
  • Mathematics
    Transformation Groups
  • 2017
We say that a polynomial automorphism ϕ in n variables is stably co-tame if the tame subgroup in n variables is contained in the subgroup generated by ϕ and affine automorphisms in n+1 variables. In

Co-tame polynomial automorphisms

It is shown that the statement "Every $m$-triangular automorphism is either affine or co-tame" is true if and only if $m \leq 3$; this improves upon positive results of Bodnarchuk and negative results of the authors.

References

SHOWING 1-8 OF 8 REFERENCES

GENERALISATIONS OF THE TAME AUTOMORPHISMS OVER A DOMAIN OF POSITIVE CHARACTERISTIC

In this paper, we introduce two generalizations of the tame subgroup of the automorphism group of a polynomial ring over a domain of positive characteristic. We study detailed structures of these new

On Generators of the Tame Invertible Polynomial Maps Group

The group TGAn of tame invertible polynomial maps is generated by the affine group AGLn and the triangular polynomic maps group Bn and some classes of polynometric maps q, which have the same property are ascertained.

The tame and the wild automorphisms of polynomial rings in three variables

Let C = F [x1, x2, . . . , xn] be the polynomial ring in the variables x1, x2, . . . , xn over a field F , and let AutC be the group of automorphisms of C as an algebra over F . An automorphism τ ∈

The Amalgamated Product Structure of the Tame Automorphism Group in Dimension Three

It is shown the the tame subgroup $\text{TA}_3(\mathbb C)$ of the group $\text{GA}_3(\mathbb C)$ of polynomials automorphisms of ${\mathbb C}^3$ can be realized as the product of three subgroups,

Über ganze birationale Transformationen der Ebene.

Coordinates of R[x,y]: Constructions and Classifications

Let R be a PID. We construct and classify all coordinates of R[x, y] of the form p 2 y + Q 2(p 1 x + Q 1(y)) with p 1, p 2 ∈ qt(R) and Q 1, Q 2 ∈ qt(R)[y]. From this construction (with R = K[z]) we

On polynomial rings in two variables

  • Nieuw. Arch. Wisk
  • 1953

On polynomial rings in two variables, Nieuw

  • Arch. Wisk
  • 1953