On the Classification of Algebras (1312.6612v1)

Published 23 Dec 2013 in math.RA

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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Authors (1)

Alex S. E. Levin

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