Analysis Seminar: "An imprimitivity theorem for Hilbert modules"

Abstract: Mackey's imprimitivity theorem identifies those unitary representations of a group G that are induced from a representation of a subgroup H: the induced representations are precisely those that carry a compatible representation of the C*-algebra C_0(G/H). Rieffel later put this result into the broader context of induced representations of C*-algebras: induced representations can in general be characterised by the existence of a compatible representation of an auxiliary C*-algebra.

In this talk I shall discuss the related problem of recognising induced Hilbert C*-modules. I shall explain why the natural auxiliary object entering into the characterisation of induced modules is a kind of C*-coalgebra, rather than a C*-algebra; and I will describe two examples in which these somewhat abstract co-algebraic objects can be put into a more familiar C*-algebraic form.

Host: Yanli Song