Non-cyclotomic Presentations of Modules and Prime-order Automorphisms of Kirchberg Algebras

2005/04/14 by Jack Spielberg, Spielberg, Jack · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Finite Group Theory Research #math.OA #math.RA

paper · pdf · doi:10.48550/arxiv.math/0504287

19 pages, 7 figures

arxiv created 2005/04/14 · arxiv updated 2009/12/01

Abstract

We prove the following theorem: let A be a UCT Kirchberg algebra, and let α be a prime-order automorphism of K_*(A), with α([1_A])=[1_A] in case A is unital. Then α is induced from an automorphism of A having the same order as α. 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.

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