Inducing Primitive Ideals

2006/01/03 by Siegfried Echterhoff, Echterhoff, Siegfried, Dana P. Williams +1
Mathematics · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Rings, Modules, and Algebras #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/0601051

17 Pages

arxiv created 2006/01/03 · openalex publication_date 2006/01/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study conditions on a C^*-dynamical system (A,G,α) under which induction of primitive ideals (resp. irreducible representations) from stabilizers for the action of G on the primitive ideal space \Prim(A) give primitive ideals (resp. irreducible representations) of the crossed product A\rtimes_αG. The results build on earlier results of Sauvageot and others, and will correct a (possibly overly optimistic) statement of the first author.

Related

• The primitive ideal space of the partial-isometric crossed product of a\n system by a single automorphism
• The ideal structure of reduced crossed products
• The primitive ideal space of the partial-isometric crossed product by automorphic actions of the semigroup ℕ²
• Ideal structure of C*-algebras of singly generated dynamical systems
• Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems