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- W4301457629 abstract "We show that the octonions can be defined as the $mathbb{R}$-algebra with basis $lbrace e^x colon x in mathbb{F}_8 rbrace$ and multiplication given by $e^x e^y = (-1)^{varphi(x,y)}e^{x + y}$, where $varphi(x,y) = operatorname{tr}(y x^6)$. While it is well known that the octonions can be described as a twisted group algebra, our purpose is to point out that this is a useful description. We show how the basic properties of the octonions follow easily from our definition. We give a uniform description of the sixteen orders of integral octonions containing the Gravesian integers, and a computation-free proof of their existence." @default.
- W4301457629 created "2022-10-05" @default.
- W4301457629 creator A5085174191 @default.
- W4301457629 date "2017-02-19" @default.
- W4301457629 modified "2023-09-27" @default.
- W4301457629 title "The octonions as a twisted group algebra" @default.
- W4301457629 doi "https://doi.org/10.48550/arxiv.1702.05705" @default.
- W4301457629 hasPublicationYear "2017" @default.
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