Saturated actions by finite dimensional Hopf *-algebras on C*-algebras

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dc.creatorJeong, J. A.
dc.creatorPark, G. H.
dc.date2007-04-12
dc.date.accessioned2026-07-07T07:56:19Z
dc.date.available2026-07-07T07:56:19Z
dc.descriptionIf a finite group action $α$ on a unital $C^*$-algebra $M$ is saturated, the canonical conditional expectation $E:M\to M^α$ onto the fixed point algebra is known to be of index finite type with $Index(E)=|G|$ in the sense of Watatani. More generally if a finite dimensional Hopf $*$-algebra $A$ acts on $M$ and the action is saturated, the same is true with $Index (E)=\dim(A)$. In this paper we prove that the converse is true. Especially in case $M$ is a commutative $C^*$-algebra $C(X)$ and $α$ is a finite group action, we give an equivalent condition in order that the expectation $E:C(X)\to C(X)^α$ is of index finite type, from which we obtain that $α$ is saturated if and only if $G$ acts freely on $X$. Actions by compact groups are also considered to show that the gauge action $γ$ on a graph $C^*$-algebra $C^*(E)$ associated with a locally finite directed graph $E$ is saturated.
dc.description18 pages, to be published in Intern. J. Math
dc.identifierhttps://arxiv.org/abs/0704.1549
dc.identifierhttp://arxiv.org/abs/0704.1549
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127268
dc.subjectOperator Algebras
dc.subject46L05
dc.titleSaturated actions by finite dimensional Hopf *-algebras on C*-algebras
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