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

It is shown that the gentle one-cycle algebra [Formula: see text] 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 [Formula: see text] is shown to be isomorphic to its Riedtmann Lie algebra.