A complete classification of three-dimensional algebras over ℝ and ℂ — 温故知新 (visiting old, learn new)-Reference-Cited by-同舟云学术

A complete classification of three-dimensional algebras over ℝ and ℂ — 温故知新 (visiting old, learn new)

Published:2020-10-16 Issue:08 Volume:14 Page:2150131
ISSN:1793-5571
Container-title:Asian-European Journal of Mathematics
language:en
Short-container-title:Asian-European J. Math.

Author:

Kobayashi Yuji¹,Shirayanagi Kiyoshi¹^ORCID,Tsukada Makoto¹,Takahasi Sin-Ei²

Affiliation:

1. Department of Information Science, Toho University, Miyama 2-2-1, Funabashi, Chiba 274-8510, Japan

2. Laboratory of Mathematics and Games, Katsushika 2-371, Funabashi, Chiba 273-0032, Japan

Abstract

We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a completely 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 and this century.

Funder

Japan Society for the Promotion of Science

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179355712150131X

Reference12 articles.

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2. On hypercomplex number systems

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5. Linear Associative Algebra

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