34 research outputs found
On twisted group C-algebras associated with FC-hypercentral groups and other related groups
We show that the twisted group C-algebra associated with a discrete
FC-hypercentral group is simple (resp. has a unique tracial state) if and only
if Kleppner's condition is satisfied. This generalizes a result of J. Packer
for countable nilpotent groups. We also consider a larger class of groups, for
which we can show that the corresponding reduced twisted group C-algebras
have a unique tracial state if and only if Kleppner's condition holds.Comment: 16 pages. Some minor changes, mostly in subsection 2.3; two
references adde
Primitivity of some full group C-algebras
We show that the full group C-algebra of the free product of two
nontrivial countable amenable discrete groups, where at least one of them has
more than two elements, is primitive. We also show that in many cases, this
C-algebra is antiliminary and has an uncountable family of pairwise
inequivalent, faithful irreducible representations.Comment: 18 pages. Preliminary version. Comments are wellcome
Free nilpotent groups are C*-superrigid
The free nilpotent group of class and rank is the free
object on generators in the category of nilpotent groups of class at most
. We show that can be recovered from its reduced group
-algebra, in the sense that if is any group such that is
isomorphic to , then must be isomorphic to .Comment: 5 pages; minor revision; to appear in Proc. Amer. Math. So
On the K-theory of C*-algebras arising from integral dynamics
We investigate the -theory of unital UCT Kirchberg algebras
arising from families of relatively prime numbers. It is
shown that is the direct sum of a free abelian group and a
torsion group, each of which is realized by another distinct -algebra
naturally associated to . The -algebra representing the torsion part is
identified with a natural subalgebra of . For
the -theory of , the cardinality of determines the free
part and is also relevant for the torsion part, for which the greatest common
divisor of plays a central role as well. In the case
where or we obtain a complete classification
for . Our results support the conjecture that
coincides with . This would lead to a complete
classification of , and is related to a conjecture about
-graphs.Comment: 27 pages; v2: minor update in 5.7; v3: some typos corrected, one
reference added, to appear in Ergodic Theory Dynam. System
Cuntz-Li algebras from a-adic numbers
The a-adic numbers are those groups that arise as Hausdorff completions of
noncyclic subgroups of the rational numbers. We give a crossed product
construction of (stabilized) Cuntz-Li algebras coming from the a-adic numbers
and investigate the structure of the associated algebras. In particular, these
algebras are in many cases Kirchberg algebras in the UCT class. Moreover, we
prove an a-adic duality theorem, which links a Cuntz-Li algebra with a
corresponding dynamical system on the real numbers. The paper also contains an
appendix where a nonabelian version of the "subgroup of dual group theorem" is
given in the setting of coactions.Comment: 41 pages; revised versio