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arXiv · 1808.02199

Classification of 7-dimensional subalgebras of 8-dimensional Clifford algebra

Uladzimir Shtukar
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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.

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Uladzimir Shtukar. 2018-08-06. Classification of 7-dimensional subalgebras of 8-dimensional Clifford algebra. https://arxiv.org/abs/1808.02199

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