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arXiv · 1605.07540

The ideal structure of algebraic partial crossed products

M. Dokuchaev·R. Exel
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Abstract

Given a partial action of a discrete group $G$ on a Hausdorff, locally compact, totally disconnected topological space $X$, we consider the correponding partial action of $G$ on the algebra $L_c(X)$ consisting of all locally constant, compactly supported functions on $X$, taking values in a given field $K$. We then study the ideal structure of the algebraic partial crossed product $L_c(X)\rtimes G$. After developping a theory of induced ideals, we show that every ideal in $L_c(X)\rtimes G$ may be obtained as the intersection of ideals induced from isotropy groups, thus proving an algebraic version of the Effros-Hahn conjecture.

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M. Dokuchaev, R. Exel. 2016-05-24. The ideal structure of algebraic partial crossed products. https://arxiv.org/abs/1605.07540

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