Absence of 15-dimensional subalgebras at 16-dimensional Clifford algebra
Uladzimir Shtukar
TL;DR
This paper proves that the 16-dimensional Clifford algebra over any field does not contain any 15-dimensional subalgebras, using canonical bases for the proof.
Contribution
It establishes a definitive non-existence result for 15-dimensional subalgebras in 16-dimensional Clifford algebras, a novel theoretical finding.
Findings
No 15-dimensional subalgebras exist in 16-dimensional Clifford algebra
Canonical bases are effective for subalgebra determination
The result holds over any field
Abstract
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.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Finite Group Theory Research · Advanced Algebra and Geometry