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October 20, 2025Open Access

On the Unique Direct Sum Decomposition of the Cl(1, 9) Clifford Algebra in a Dynamic-Algebraic Framework

Puntos clave

The study establishes a unique direct sum decomposition of Cl(1,9), emphasizing its algebraic structure and relevance.
Key findings include a central subalgebra isomorphic to Cl(1,3), explaining its connection to Minkowski spacetime.
Using idempotent elements, a formal framework is provided that links algebraic concepts to mathematical physics.
The results potentially enhance understanding in theoretical cosmology, bridging algebraic structures with geometric principles.

Resumen

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 (Fri,) studied this question.

www.synapsesocial.com/papers/68f5fcdc8d54a28a75cf23e4 — DOI: https://doi.org/10.20944/preprints202510.1305.v1

On the Unique Direct Sum Decomposition of the Cl(1, 9) Clifford Algebra in a Dynamic-Algebraic Framework

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