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arXiv · 1312.6612

On the Classification of Algebras

Alex S. E. Levin
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Abstract

We classify (possibly non commutative) algebras of low rank over a domain R. We first review results for algebras of rank 2 and for finite-dimensional division algebras over the real numbers. These results motivate us to consider which algebras possess a standard involution. Our main result is that algebras of rank 3 are either commutative or possess a standard involution.

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Alex S. E. Levin. 2013-12-23. On the Classification of Algebras. https://arxiv.org/abs/1312.6612

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