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Let k be a field. Let R be a finite-dimensional k-algebra with centre k which is representation-finite and hereditary; thus R is Morita equivalent to the tensor algebra of a k-species with underlying graph A a disjoint union of Dynkin diagrams, and the set of isomorphism classes of indecomposable R-modules corresponds bijectively to the set @+ of positive roots of the corresponding semisimple complex Lie algebra g (see [G] and [DRl ] ). Consequently, the Grothendieck group K( R mod) of all finitely generated R-modules modulo split exact sequences is the free abelian group with basis indexed by @ +. Let h be a Cartan subalgebra of g and g = n + @ h 0 n _ the corresponding triangular decomposition. Note that n+ is the direct sum of one-dimensional complex vectorspaces indexed by the elements of @ +, so we may identify K(R mod) Q @ and n + as vectorspaces, and we deal with the problem of how to recover the Lie multiplication of n, on K( R mod). We have shown in [R2] that the Grothendieck group K(R mod) may be considered in a natural way as a Lie algebra by using as structure constants the evaluations of Hall polynomials at 1. The aim of this paper is to show that this Lie algebra K(R mod) can be identified with a Chevalley H-form of n + ; in particular K( R mod) @ @ and n+ are isomorphic as Lie algebras. We are going to determine all possible polynomials which occur as Hall polynomials ~p;;~, where x, y, z E @ + . There are precisely 16 different polynomials (including the zero polynomial cpO), and the absolute value of their evaluations at 1 is bounded by 3. One easily observes that q;X = 0 in case y #z +x; thus let us assume y = z + x. In this case, precisely one of the two polynomials cp,‘, and cpzZ is non-zero. The non-zero polynomials cp;’ can be written in the form irqi, where [, = C’:i T’, with 1 d r 6 3, and (pi is one of the following 12 integral polynomials