On the Ringel--Hall algebra of the gentle one-cycle algebra $Λ(n-1,1,1)$

Abstract: It is shown that the gentle one-cycle algebra $\Lambda(n-1,1,1)$ has Hall polynomials. The Hall polynomials are explicitly given for all triples of indecomposable modules, and as a consequence, the Ringel--Hall Lie algebra of $\Lambda(n-1,1,1)$ is shown to be isomorphic to its Riedtmann Lie algebra.