Non-cyclotomic presentations of modules and prime-order automorphisms of Kirchberg algebras

✍ Scribed by Spielberg, Jack

• Book ID: 118740432
• Publisher: Walter de Gruyter GmbH & Co. KG
• Year: 2007
• Tongue: English
• Weight: 210 KB
• Volume: 2007
• Category: Article
• ISSN: 0075-4102
• DOI: 10.1515/CRELLE.2007.098

✦ Synopsis

We prove the following theorem: let A be a UCT Kirchberg algebra, and let a be a prime-order automorphism of K Ã ðAÞ, with að½1 A Þ ¼ ½1 A in case A is unital. Then a is induced from an automorphism of A having the same order as a. This result is extended to certain instances of an equivariant inclusion of Kirchberg algebras. As a crucial ingredient we prove the following result in representation theory: every module over the integral group ring of a cyclic group of prime order has a natural presentation by generalized lattices with no cyclotomic summands.