Generalised bosonic construction of Virasoro algebras

Energy-momentum tensors of conformal field theories and some of their primary fields, including those of parafermionic theories based on simply-laced Lie algebras, are constructed from free bosons. The classification of such theories requires a generalisation of the root systems of Lie algebras. The complete list of such energy-momentum tensors, that can be constructed from two free bosons, includes those of the first four c < 1 theories. (orig.)