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

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

1996-02-07

arxiv.org/abs/funct-an/9602004v2

Mathematics

Operator Algebras

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

Scientific paper

Consider a coaction $\delta$ 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 $A\times_{\delta|}G/N$ and $A\times_\delta G\times_{\deltahat,r}N$ 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.

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