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Affine Circle Geometry over Quaternion Skew Fields

Hans Havlicek

TL;DR

The affine circle geometry arising from a quaternion skew field and one of its maximal commutative subfields is investigated.

Abstract

We investigate the a{\pm}ne circle geometry arising from a quaternion skew field and one of its maximal commutative subfields.

Affine Circle Geometry over Quaternion Skew Fields

TL;DR

The affine circle geometry arising from a quaternion skew field and one of its maximal commutative subfields is investigated.

Abstract

We investigate the a{\pm}ne circle geometry arising from a quaternion skew field and one of its maximal commutative subfields.

Paper Structure

This paper contains 3 sections, 7 theorems, 51 equations.

Table of Contents

  1. Introduction
  2. Projective Chain Geometry on $L/K$
  3. Affine Circle Geometry on $L/K$

Key Result

Lemma 1

Let ${\bf W}$ be a right vector space over $K$, $\dim{\bf W}=2$, and let $\{{\bf u},{\bf v}\}$ be a basis of ${\bf W}$. Then is an affine Baer subplane (over $Z$) of the affine plane on ${\bf W}$.

Theorems & Definitions (7)

  • Lemma 1
  • Theorem 1
  • Lemma 2
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5