Published December 31, 2025 | Version version 1
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Unified Analytic Solution of Polynomial Equations in Non-Commutative C*-Algebraic Closure: A Comprehensive Extension from Clifford Algebras with Complete Mathematical Foundations

Authors/Creators

  • 1. ROR icon Peking University

Description

This paper presents a comprehensive extension of the differential and algebraic framework for solving polynomial equations from Clifford algebras to the more general setting of non-commutative C* algebras. We systematically address the fundamental challenges posed by non-commutativity and infinite dimensional structure through the rigorous introduction of a path-ordering operator P that projects onto symmetric subspaces while preserving essential C*-algebraic structure. We establish a complete theoretical foundation for solving systems of multivariate polynomial equations defined within a non-commutative C*-algebra A by constructing a non-commutative C*-algebraic closure VncA.We provide complete constructive proofs with full mathematical rigor, including detailed derivations of non-commutative Newton identities and convergence analysis in C*-algebraic settings. The algorithms developed achieve well-defined computational complexity with comprehensive error analysis. Numerical validation demonstrates precision across various test cases in finite-dimensional C*-algebras. The work reconciles with classical impossibility results while demonstrating that explicit analytic solutions exist in appropriately extended algebraic structures that incorporate differential and operator-theoretic operations within a non-commutative C*-algebraic framework.

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Alternative title (English)
Unified Analytic Solution of Polynomial Equations in Non-Commutative C*-Algebraic Closure

Dates

Submitted
2025-12-31

References

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