On the Ringel--Hall algebra of the gentle one-cycle algebra $\mathrm{\Lambda }(n-1,1,1)$

It is shown that the gentle one-cycle algebra $\mathrm{\Lambda }(n-1,1,1)$ 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 $\mathrm{\Lambda }(n-1,1,1)$ is shown to be isomorphic to its Riedtmann Lie algebra.