Abstract: Given a connected compact Lie group G and a degree 4 cohomology class of its classifying space, one obtains a central extension of the loop group LG by a procedure known as ?transgression?. K. Waldorf proved that this procedure is reversible if one remembers the ?fusion structure? on the central extension. In this talk, I will explain an analogue of Waldorf?s theorem in the context of algebraic geometry.