A
-algebra
is said to have the ideal property if each closed two-sided ideal of
is
generated as a closed two-sided ideal by the projections inside the ideal.
-algebras
with the ideal property are a generalization and unification of real rank zero
-algebras and unital
simple
-algebras.
It was long expected that an invariant that we call
, consisting of the scaled
ordered total
-group
(used in the real rank zero case), along with the tracial state spaces
for each cut-down
algebra
, as part of the
Elliott invariant of
(for each
), with
certain compatibility conditions, is the complete invariant for a certain well behaved class of
-algebras with the
ideal property (e.g.,
algebras with no dimension growth). In this paper, we construct two nonisomorphic
algebras
and
with the ideal
property such that
,
disproving this conjecture. The invariant to distinguish the
two algebras is the collection of Hausdorffified algebraic
-groups
(for
each
),
along with certain compatibility conditions. We will prove in a separate article that,
after adding this new ingredient, the invariant becomes the complete invariant for
algebras (of no dimension growth) with the ideal property.
PDF Access Denied
We have not been able to recognize your IP address
18.97.14.88
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.