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Classification of Left Octonionic Modules
Advances in Applied Clifford Algebras ( IF 1.1 ) Pub Date : 2021-01-21 , DOI: 10.1007/s00006-020-01113-4
Qinghai Huo , Yong Li , Guangbin Ren

In this article, we provide a complete classification of left octonionic modules (finite or infinite dimensions) in terms of new notions such as associative elements and conjugate associative elements. We give a simple approach to determine the irreducible left \(\mathbb {O}\)-modules by utilizing the Clifford algebra \(C\ell _{7}\). We find that every left \(\mathbb {O}\)-module has a basis in some sense. This means that every left \(\mathbb {O}\)-module is a “free” module.



中文翻译:

左八键模块的分类

在本文中,我们根据新概念(例如,关联元素和共轭关联元素)提供了一个完整的左张回音模块分类(有限或无限尺寸)。我们给出一种简单的方法,通过利用Clifford代数\(C \ ell _ {7} \)来确定不可约的左\(\ mathbb {O} \) -模。我们发现每个左\(\ mathbb {O} \)-模块在某种意义上都有一个基础。这意味着每个左\(\ mathbb {O} \)-模块都是一个“免费”模块。

更新日期:2021-01-21
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