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On induced covariant systems. (English) Zbl 0692.46054
Let H be a closed subgroup of a locally compact group G such that H acts strongly continuously by *-automorphism on a $$C^*$$-algebra D. The symbol Ind D denotes the induced $$C^*$$-algebra.
It is known that there is a continuous G-invariant map $$\phi$$ : prim(Ind D)$$\to G/H$$, which is defined by $$\phi (J)=xH$$ if J contains the ideal $$I(x)=\{f\in Ind D:$$ $$f(x)=0\}.$$
In this note the author shows the converse of this proposition namely that if (G,A) is a covariant system and if $$I=\cap \{J:\quad J\in \phi^{-1}(\{eH\})\}$$ and $$D=A/I$$, then (G,A) is isomorphic to (G,Ind D). Here the G-equivariant isomorphism $$\phi$$ : $$A\to ind D$$ is specified. In addition, there are two interesting corollaries.
Reviewer: J.C.Rho

##### MSC:
 46L55 Noncommutative dynamical systems 46L05 General theory of $$C^*$$-algebras 22D30 Induced representations for locally compact groups
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##### References:
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