On the Classification of Algebras

2013/12/23 by Alex S. E. Levin, Levin, Alex S. E.
Mathematics · #Algebraic structures and combinatorial models #Rings, Modules, and Algebras #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1312.6612

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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