On the Classification of Algebras
Rings and Algebras
2013-12-24 v1
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.
Keywords
Cite
@article{arxiv.1312.6612,
title = {On the Classification of Algebras},
author = {Alex S. E. Levin},
journal= {arXiv preprint arXiv:1312.6612},
year = {2013}
}
Comments
Master's Thesis, University of Vermont, May 2013. Advisor: John Voight