Affine Lie algebras and tame quivers

Abstract.

C.M. Ringel defined a Hall algebra associated with the category of representations of a quiver of Dynkin type and gave an explicit description of the structure constants of the corresponding Lie algebra. We utilize functorial properties of the Hall algebra to give a simple proof of the Ringel's result, and to generalize it to the case of a quiver of affine type. In particular a linear spanning set of the positive part of an affine Lie algebra and the corresponding structure constants are described in terms of quivers.