Classification of Left Octonionic Modules

Classification of Left Octonionic Modules

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 O -modules by utilizing the Clifford a...

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Veröffentlicht in:Advances in applied Clifford algebras 2021-02, Vol.31 (1), Article 11
Hauptverfasser: Huo, Qinghai, Li, Yong, Ren, Guangbin
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Classification
Mathematical and Computational Physics
Mathematical Methods in Physics
Modules
Physics
Physics and Astronomy
Theoretical
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Zusammenfassung: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 O -modules by utilizing the Clifford algebra C ℓ 7 . We find that every left O -module has a basis in some sense. This means that every left O -module is a “free” module.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-020-01113-4