Gauged supergravity in the embedding tensor formalism gives rise to a tensor hierarchy of gauge parameters, potentials and field strengths. I will show that the relations between these tensors can be compactly expressed in terms of a Lie superalgebra, which is an infinite-dimensional extension of the global symmetry Lie algebra. The talk is based on the papers 1308.4972 (with J. Greitz and P. Howe) and 1305.0018.