This shows how the central extension M 0 of the non-semi-simple and finite-dimensional Schrödinger algebra becomes a component of an infinite family in the Schrödinger–Virasoro algebra. In addition, and in analogy with either the Virasoro algebra or the Kac–Moody algebra, further central extensions are possible. However, a non-vanishing result only exists for the commutator [ X n , X n ′ ] , where it must be of the familiar Virasoro form, namely