Journal of Operator Theory

Volume 46, Issue 1, Summer 2001 pp. 99-122.

The Ext class of an approximately inner automorphism. II

Authors: A. Kishimoto (1), and A. Kumjian
Author institution: (1) Department of Mathematics, Hokkaido University, Sapporo 060, Japan
(2) Department of Mathematics, University of Nevada, Reno, NV 89557, USA

Summary: Let

$A$ be a simple unital AT algebra of real rank zero and Inn(

$A$ ) the group of inner automorphisms of

$A$ . In the previous paper we have shown that the natural map of the group

$\Ap$ of approximately inner automorphisms into

$\Ext({\rm K}_1(A),{\rm K}_0(A))\oplus\Ext({\rm K}_0(A),{\rm K}_1(A))$ is surjective; the kernel of this map includes the subgroup of automorphisms which are homotopic to

$\Inn$ . In this paper we consider the quotient of

$\Ap$ by the smaller normal subgroup

$\AI$ which consists of asymptotically inner automorphisms and describe it as

$\OExt({\rm K}_1(A),{\rm K}_0(A))\oplus \Ext({\rm K}_0(A),{\rm K}_1(A)),$ where

$\OExt({\rm K}_1(A),{\rm K}_0(A))$ is a kind of extension group which takes into account the fact that

${\rm K}_0(A)$ is an ordered group and has the usual Ext as a quotient.

Contents Full-Text PDF