What question did this study set out to answer?

This work aims to investigate the path algebra and representation theory associated with a specific four-node quiver.

July 29, 2026Open Access

A Four-Node Quiver: Path Algebra, Cycle Relations, and Representation Theory

View Full Paper

Ask AI

Bookmark

Authors

Explores the path algebra and representation theory within a four-node quiver, revealing important algebraic structures.

This work aims to investigate the path algebra and representation theory associated with a specific four-node quiver.
Defines the quiver and its adjacency matrix
Derives graph-theoretic properties and computes graded dimensions of the path algebra
Analyzes representation category under specific constraints and classifies indecomposable representations.
Establishes that the quotient algebra A is well-defined and computes its graded dimensions
Proves the boundedness of indecomposable representations in the representation category Rep(A, κ)
Reports the asymptotic growth rates of path counts and highlights infinite mutation type properties of the quiver.

Arthur Stewart (2026) studied this question.

View Full Paper

Ask AI

Bookmark