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2021•International Journal of Algebra and ComputationRequires access

Some co-tame automorphisms of affine spaces

Dayan Liu, Fumei Liu, Xiaosong Sun

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Abstract

The investigation of co-tame automorphisms of the affine space [Formula: see text] is helpful to understand the structure of its automorphisms group. In this paper, we show the co-tameness of several classes of automorphisms, including some 3-parabolic automorphisms, power-linear automorphisms, homogeneous automorphisms in small dimension or small transcendence degree. We also classify all additive-nilpotent automorphisms in dimension four and show that they are co-tame.

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What this paper is about

The investigation of co-tame automorphisms of the affine space [Formula: see text] is helpful to understand the structure of its automorphisms group. In this paper, we show the co-tameness of several classes of automorphisms, including some 3-parabolic automorphisms, power-linear automorphisms, homogeneous automorphisms in small dimension or small transcendence degree. We also classify all additive-nilpotent automorphisms in dimension four and show that they are co-tame.

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Available abstract

The investigation of co-tame automorphisms of the affine space [Formula: see text] is helpful to understand the structure of its automorphisms group. In this paper, we show the co-tameness of several classes of automorphisms, including some 3-parabolic automorphisms, power-linear automorphisms, homogeneous automorphisms in small dimension or small transcendence degree. We also classify all additive-nilpotent automorphisms in dimension four and show that they are co-tame.

Key concepts: Automorphism, Mathematics, Automorphisms of the symmetric and alternating groups, Pure mathematics, Dimension (graph theory), Nilpotent, Affine transformation, Space (punctuation)

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