Duality of Restriction and Induction for $C^*$-Coactions

Kaliszewski, S.; Quigg, John; Raeburn, Iain

Duality of Restriction and Induction for $C^*$-Coactions

Authors

Kaliszewski, S.

Quigg, John

Raeburn, Iain

Description

Consider a coaction $δ$ of a locally compact group $G$ on a \cstar algebra $A$, and a closed normal subgroup $N$ of $G$. We prove, following results of Echterhoff for abelian $G$, that Mansfield's imprimitivity between $A\times_{δ|}G/N$ and $A\times_δG\times_{\deltahat,r}N$ implements equivalences between Mansfield induction of representations from $A\times G/N$ to $A\times G$ and restriction of representations from $A\times G\times_r N$ to $A\times G$, and between restriction of representations from $A\times G$ to $A\times G/N$ and Green induction of representations from $A\times G$ to $A\times G\times_r N$. This allows us to deduce properties of Mansfield induction from the known theory of ordinary crossed products.
42 pages, LaTeX 2e, requires amscd.sty and pb-diagram.sty. Revisions include amendment of the proofs of Theorems 3.1, 4.1, 5.2 and 5.4, which had relied on the false Lemma 2.3 in [KQ95]. Two new lemmas have been inserted early in Section 5 to facilitate this