Induction in stages for crossed products of C*-algebras by maximal coactions

摘要

Let 6 be a maximal coaction of a locally compact group G on a C*-algebra B, and let N and H be closed normal subgroups of G with N C H. We show that the process Ind(G/H)(G) which uses Mansfield's bimodule to induce representations of B x delta G from those of B x delta vertical bar (G/H) is equivalent to the two-stage G/N induction process Ind(G/N)(G) o Ind(G/H)(G/N). The proof involves a calculus of symmetric imprimitivity bimodules which relates the bimodule tensor product to the fibred product of the underlying spaces. (C) 2007 Elsevier Inc. All rights reserved.