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

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

2005-04-14

arxiv.org/abs/math/0504287v1

Mathematics

Operator Algebras

19 pages, 7 figures

Scientific paper

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