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arXiv · 1903.01623

A complete classification of three-dimensional algebras over ${\mathbb R}$ and ${\mathbb C}$

Yuji Kobayashi·Kiyoshi Shirayanagi·Sin-Ei Takahasi·Makoto Tsukada
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Abstract

We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a complete elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We compare our results with those given by mathematicians in the 19th century.

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Yuji Kobayashi, Kiyoshi Shirayanagi, Sin-Ei Takahasi, Makoto Tsukada. 2019-03-05. A complete classification of three-dimensional algebras over ${\mathbb R}$ and ${\mathbb C}$. https://arxiv.org/abs/1903.01623

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