Abstract
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.
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The authors would like to thank the referees for the very detailed comments and correct suggestions that really helped to improve this paper.
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Communicated by Jacques Helmstetter.
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This work was supported by the NNSF of China (11771412).
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Huo, Q., Li, Y. & Ren, G. Classification of Left Octonionic Modules. Adv. Appl. Clifford Algebras 31, 11 (2021). https://doi.org/10.1007/s00006-020-01113-4
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DOI: https://doi.org/10.1007/s00006-020-01113-4