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A complete classification of three-dimensional algebras over ${\mathbb R}$ and ${\mathbb C}$ (1903.01623v1)
Published 5 Mar 2019 in math.RA
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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