Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems

2023/01/03 by Are Austad, Austad, Are, Sven Raum +1 · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2301.01027

openalex publication_date 2023/01/03 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28

Abstract

We introduce the ℓ¹-ideal intersection property for crossed product C*-algebras. It is implied by C*-simplicity as well as C*-uniqueness. We show that topological dynamical systems of arbitrary lattices in connected Lie groups, arbitrary linear groups over the integers in a number field and arbitrary virtually polycyclic groups have the ℓ¹-ideal intersection property. On the way, we extend previous results on C*-uniqueness of L¹-groupoid algebras to the general twisted setting.

Cited by

• Strict comparison for twisted group C*-algebras
• A Banach *-algebra associated with the action of a group on a topological space

Related

• The ideal structure of reduced crossed products
• Primality and the ideal intersection property for reduced crossed products
• Reduced twisted crossed products over C*-simple groups
• Uniformly recurrent subgroups and the ideal structure of reduced crossed products
• The structure of crossed products by endomorphisms