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SUMMARY:Endomorphisms and automorphisms of the 2-adic ring C*-algebra Q_2 
 - Stefano Rossi (Università degli Studi di Roma Tor Vergata)
DTSTART:20170216T140000Z
DTEND:20170216T150000Z
UID:TALK70948@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The 2-adic ring C*-algebra is the universal C*-algebra Q_2 gen
 erated by an isometry S_2 and a unitary 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&#39\;ll start by discussing some nice properties of this in
 clusion\, as they came to be pointed out in a recent joint work with V. Ai
 ello and R. Conti. Among other things\, the inclusion enjoys a kind of rig
 idity property\, i.e.\, any endomorphism of the larger that restricts triv
 ially to the smaller must be trivial itself. I&#39\;ll also say a word or 
 two about the extension problem\, which is concerned with extending an end
 omorphism 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 endomorphisms 
 (automophisms indeed!) show up as soon as the so-called Bogoljubov automor
 phisms of O_2 are looked at. Then I&#39\;ll move on to particular classes 
 of endomorphisms and automorphisms of Q_2\, including those fixing the dia
 gonal D_2. Notably\, the semigroup of the endomorphisms fixing U turns out
  to be a maximal abelian group isomorphic with the group of continuous fun
 ctions from the one-dimensional torus to itself. Such an analysis\, though
 \, calls for some knowledge of the inner structure of Q_2.&nbsp\; More pre
 cisely\, it&#39\;s vital to prove that C*(U) is a maximal commutative suba
 lgebra. Time permitting\, I&#39\;ll also try to present forthcoming genera
 lizations to broader classes of C*-algebras\, on which we&#39\;re currentl
 y working with N. Stammeier as well.<br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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