We review the passage from the supermembrane to matrix theory via a
consistent truncation following a non-commutative deformation in light-cone
gauge. Some indications are given that there should exist a generalisation of
non-commutativity involving a three-index theta on the membrane, and we discuss
some possible ways of investigating the corresponding algebraic structure.Comment: 11 pp, plain tex. Invited talk presented at the conference
``Non-Commutative Geometry and Representation Theory in Mathematical
Physics'', Karlstad, Sweden, July 5-10, 200
