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Triangular involutions of the four-dimensional polynomial ring in characteristic two

Ryuji Tanimoto

Abstract

We are concerned with polynomial involutions in characteristic two. In this note, we look for involutions among triangular automorphisms of the four-dimensional polynomial ring in characteristic two and obtain three types of such involutions.

Triangular involutions of the four-dimensional polynomial ring in characteristic two

Abstract

We are concerned with polynomial involutions in characteristic two. In this note, we look for involutions among triangular automorphisms of the four-dimensional polynomial ring in characteristic two and obtain three types of such involutions.

Paper Structure

This paper contains 4 sections, 3 theorems, 12 equations.

Table of Contents

  1. Proof of (1)
  2. Proof of (2)
  3. Proof of the implication $(2.1) \Longrightarrow (2.2)$
  4. Proof of the implication $(2.2) \Longrightarrow (2.1)$

Key Result

Theorem 1

Assume that the characteristic of $k$ is two. Then the following assertions (1) and (2) hold true:

Theorems & Definitions (5)

  • Theorem 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof