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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Endomorphisms and automorphisms of the 2-adic ring
C*-algebra Q_2 - Stefano Rossi (Università degli
Studi di Roma Tor Vergata)
DTSTART;TZID=Europe/London:20170216T140000
DTEND;TZID=Europe/London:20170216T150000
UID:TALK70948AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/70948
DESCRIPTION:The 2-adic ring C*-algebra is the universal C*-alg
ebra Q_2 generated by an isometry S_2 and a unitar
y U such that S_2U=U^2S_2 and S_2S_2^*+US_2S_2^*U^
*=1. By its very definition it contains a copy of
the Cuntz algebra O_2. I'\;ll start by discussi
ng some nice properties of this inclusion\, as the
y came to be pointed out in a recent joint work wi
th V. Aiello and R. Conti. Among other things\, th
e inclusion enjoys a kind of rigidity property\, i
.e.\, any endomorphism of the larger that restrict
s trivially to the smaller must be trivial itself.
I'\;ll also say a word or two about the extens
ion problem\, which is concerned with extending an
endomorphism of O_2 to an endomorphism of Q_2. As
a matter of fact\, this is not always the case: a
wealth of examples of non-extensible endomorphism
s (automophisms indeed!) show up as soon as the so
-called Bogoljubov automorphisms of O_2 are looked
at. Then I'\;ll move on to particular classes
of endomorphisms and automorphisms of Q_2\, includ
ing those fixing the diagonal D_2. Notably\, the s
emigroup of the endomorphisms fixing U turns out t
o be a maximal abelian group isomorphic with the g
roup of continuous functions from the one-dimensio
nal torus to itself. Such an analysis\, though\, c
alls for some knowledge of the inner structure of
Q_2. \; More precisely\, it'\;s vital to pr
ove that C*(U) is a maximal commutative subalgebra
. Time permitting\, I'\;ll also try to present
forthcoming generalizations to broader classes of
C*-algebras\, on which we'\;re currently workin
g with N. Stammeier as well.

LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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