Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2024-08-31 DOI:10.1007/s00006-024-01346-7

Marek Stodola, Jaroslav Hrdina

引用次数: 0

Abstract

Using the classification of Clifford algebras and Bott periodicity, we show how higher geometric algebras can be realized as matrices over classical low dimensional geometric algebras. This matrix representation allows us to use standard geometric algebra software packages more easily. As an example, we express the geometric algebra for conics (GAC) as a matrix over the Compass ruler algebra (CRA).

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高阶几何代数及其利用底周期性的实现

利用克利福德代数和底周期性的分类，我们展示了高等几何代数如何以矩阵的形式实现经典低维几何代数。这种矩阵表示法可以让我们更轻松地使用标准几何代数软件包。例如，我们将圆锥几何代数（GAC）表述为 Compass 尺规代数（CRA）上的矩阵。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.