Open AccessA complete classification of three-dimensional algebras over ℝ and ℂ — 温故知新 (visiting old, learn new)
Author(s) -
Yuji Kobayashi,
Kiyoshi Shirayanagi,
Makoto Tsukada,
Sin–Ei Takahasi
Publication year - 2020
Publication title -
asia-european journal of mathematics/asian-european journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.294
H-Index - 14
eISSN - 1793-5571
pISSN - 1793-7183
DOI - 10.1142/s179355712150131x
Subject(s) - associative property , isomorphism (crystallography) , multiplication (music) , algebra over a field , mathematics , arithmetic , computer science , pure mathematics , combinatorics , chemistry , crystal structure , crystallography
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.