Mathematical proof reveals the direct sum decomposition of Cl(1,9) Clifford algebra, suggesting connections to the central subalgebra Cl(1,3) and Minkowski spacetime.
We present a rigorous mathematical proof of the unique direct sum decomposition of the Cl(1,9) Clifford algebra using idempotent elements. This decomposition reveals a rich algebraic structure including a central subalgebra isomorphic to Cl(1,3), corresponding to Minkowski spacetime. The results provide a formal framework potentially relevant to geometric and algebraic approaches in mathematical physics and theoretical cosmology.
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S. A. Omel’chenko (2025) studied this question.
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