A complete classification of three-dimensional algebras over ${\mathbb R}$ and ${\mathbb C}$
Rings and Algebras
2019-03-06 v1
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.
Cite
@article{arxiv.1903.01623,
title = {A complete classification of three-dimensional algebras over ${\mathbb R}$ and ${\mathbb C}$},
author = {Yuji Kobayashi and Kiyoshi Shirayanagi and Sin-Ei Takahasi and Makoto Tsukada},
journal= {arXiv preprint arXiv:1903.01623},
year = {2019}
}