Physical ageing and new representations of some Lie algebras of local scale-invariance

Indecomposable but reducible representations of several Lie algebras of local scale-transformations, including the Schr\"odinger and conformal Galilean algebras, and some of their applications in physical ageing are reviewed. The physical requirement of the decay of co-variant two-point functions for large distances is related to analyticity properties in the coordinates dual to the physical masses or rapidities.