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Duality of restriction and induction for -coactions

Authors:	S Kaliszewski John Quigg Iain Raeburn

Institution:	Department of Mathematics, University of Newcastle, Newcastle, New South Wales 2308, Australia ; Department of Mathematics, Arizona State University, Tempe, Arizona 85287 ; Department of Mathematics, University of Newcastle, Newcastle, New South Wales 2308, Australia

Abstract:	Consider a coaction $\delta$ of a locally compact group on a - algebra , and a closed normal subgroup of . We prove, following results of Echterhoff for abelian , that Mansfield's imprimitivity between $A\times _{\delta \|}G/N$ and $A\times _\delta G\times _{\hat {\delta } ,r}N$ implements equivalences between Mansfield induction of representations from $A\times _{\delta \|}G/N$ to $A\times _\delta G$ and restriction of representations from $A\times _\delta G\times _{\hat {\delta } ,r}N$ to $A\times _\delta G$ , and between restriction of representations from $A\times _\delta G$ to $A\times _{\delta \|}G/N$ and Green induction of representations from $A\times _\delta G$ to $A\times _\delta G\times _{\hat {\delta } ,r}N$ . This allows us to deduce properties of Mansfield induction from the known theory of ordinary crossed products.

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