Abstract
We present formulas for the structure constants (Hall numbers) of the Hall algebra \(+AFw-mathcal{H}(kK)\) associated to the Kronecker algebra. The formulas which in some cases involve the classical Hall polynomials \(g^{+AFw-lambda}_{(r)+AFw-mu}\) enable us to determine every Hall number. Using again these formulas we construct new PBW-bases with simple structure constants for the composition algebra \(+AFw-mathcal{C}(kK)\), making possible the definition of the generic composition algebra via Hall polynomials.
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