Affine Lie algebras play an important role in string theory and two-dimensional conformal field theory due to the way they are constructed: starting from a simple Lie algebra formula_1, one considers the loop algebra, formula_2, formed by the formula_1-valued functions on a circle (interpreted as the closed string) with pointwise commutator. The affine Lie algebra formula_4 is obtained by adding one extra dimension to the loop algebra and modifying a commutator in a non-trivial way, which physicists call a quantum anomaly (in this case, the anomaly of the WZW model) and mathematicians a central extension. More generally,