On the Ringel–Hall Algebra of the Gentle One-Cycle Algebra Λ( n− 1, 1,1)

Key Points

• To examine the Hall polynomials of the gentle one-cycle algebra and their implications for its associated Lie algebras.
• Analyzed Hall polynomials for all triples of indecomposable modules in the gentle one-cycle algebra.
• Established an isomorphism between the Ringel–Hall Lie algebra and the Riedtmann Lie algebra.
• Hall polynomials were explicitly determined for all triples of indecomposable modules.
• Confirmed the isomorphism between the Ringel–Hall Lie algebra and the Riedtmann Lie algebra.