The ideal structure of algebraic partial crossed products

2016/05/24 by Mikhailo Dokuchaev, Dokuchaev, M., R. Exel +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1605.07540

openalex publication_date 2016/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The primitive ideals of some étale groupoid C*-algebras

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