Simple Purely Infinite C*-Algebras and n-Filling Actions

✍ Scribed by Paul Jolissaint; Guyan Robertson

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 244 KB
• Volume: 175
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2000.3608

✦ Synopsis

Let n be a positive integer. We introduce a concept, which we call the n-filling property, for an action of a group on a separable unital C*-algebra A. If A=C(0) is a commutative unital C*-algebra and the action is induced by a group of homeomorphisms of 0 then the n-filling property reduces to a weak version of hyperbolicity. The n-filling property is used to prove that certain crossed product C*-algebras are purely infinite and simple. A variety of group actions on boundaries of symmetric spaces and buildings have the n-filling property. An explicit example is the action of 1=SL n (Z) on the projective n-space.