Absence of 15-dimensional subalgebras at 16-dimensional Clifford algebra
It is shown that the 16-dimensional Clifford algebra over any field has no one 15-dimensional subalgebra. Canonical bases are used throughout the determination.
math.RA↗
arXiv subjects
Uladzimir Shtukar
Publications and source records attributed to Uladzimir Shtukar.
Classification of 7-dimensional subalgebras of 8-dimensional Clifford algebra
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.
math.RA↗