Classification of 7-dimensional subalgebras of 8-dimensional Clifford algebra
Rings and Algebras
2018-08-08 v1
Abstract
All 7-dimensional subalgebras of the 8-dimensional Clifford algebra over the field C of complex numbers are found. Canonical bases are used throughout the determination. It is found that the 8-dimensional Clifford algebra over C has exactly eight 7-dimensional subalgebras and each of these eight is over the complex numbers. It follows that the 8-dimensional Clifford algebra over C has no 7-dimensional subalgebra over the real numbers. Another consequence is that the eight 7-dimensional subalgebras of the 8-dimentional Clifford over C are in fact 7-dimensional subalgebras of all greater dimensional Clifford algebras over C.
Cite
@article{arxiv.1808.02199,
title = {Classification of 7-dimensional subalgebras of 8-dimensional Clifford algebra},
author = {Uladzimir Shtukar},
journal= {arXiv preprint arXiv:1808.02199},
year = {2018}
}
Comments
8 pages. arXiv admin note: text overlap with arXiv:1808.02198