2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54838We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of chiral algebras are investigated. A crucial role is played by the mathematical structures of twining characters and orbit Lie algebras.7 pages, LaTeX, Talk given by J. Fuchs at the XXI International Colloquium on Group Theoretical Methods in Physics, (Goslar, Germany, July 1996)High Energy Physics - Theorytext