3 research outputs found
C*-algebras associated with endomorphisms and polymorphisms of compact abelian groups
A surjective endomorphism or, more generally, a polymorphism in the sense of
\cite{SV}, of a compact abelian group induces a transformation of .
We study the C*-algebra generated by this operator together with the algebra of
continuous functions which acts as multiplication operators on .
Under a natural condition on the endo- or polymorphism, this algebra is simple
and can be described by generators and relations. In the case of an
endomorphism it is always purely infinite, while for a polymorphism in the
class we consider, it is either purely infinite or has a unique trace. We prove
a formula allowing to determine the -theory of these algebras and use it to
compute the -groups in a number of interesting examples.Comment: 25 page
On Vershikian and I-cosy random variables and filtrations
peer reviewedWe prove that the equivalence between Vershik’s standardness criterion
and the I-cosiness criterion for a filtration in discrete, negative
time, holds separately for each random variable. This gives a strengthening
and a more direct proof of the global equivalence between these
two criteria. We also provide more elementary original propositions
on Vershik’s standardness criterion, while emphasizing that similar
statements for I-cosiness are sometimes not so obvious