Duality of Restriction and Induction for C ∗ -Coactions
Abstract
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
×
δ|
G/N
and $A\times_\delta G\times_{\deltahat,r}N$ implements equivalences between Mansfield induction of representations from
A×G/N
to
A×G
and restriction of representations from
A×G
×
r
N
to
A×G
, and between restriction of representations from
A×G
to
A×G/N
and Green induction of representations from
A×G
to
A×G
×
r
N
. This allows us to deduce properties of Mansfield induction from the known theory of ordinary crossed products.