What question did this study set out to answer?

The research aims to construct and analyze the path algebra of a four-node quiver relating to foundational mathematics.

July 27, 2026Open Access

The Path Algebra of The Endomorphism

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Constructs a path algebra exploring the interactions of foundational mathematics in quivers, suggesting novel algebraic structures.

The research aims to construct and analyze the path algebra of a four-node quiver relating to foundational mathematics.
Constructed the path algebra kQ of a four-node quiver with directed edges.
Computed the quotient by binary cycle relations and evaluated the resulting algebra.
Identified connections to existing research in quantum groups and cluster algebras.
The graded components of cycles recover the counts 4ⁿ, confirming algebraic robustness.
Finding that the cycle generators do not satisfy Coxeter braid relations indicates algebraic expressive limits.
Identified unique bilinear forms consistent with foundational operations and connections to Lie algebra structures.

Arthur Stewart (2026) studied this question.

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