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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Endomorphisms and automorphisms of the 2-adic ring C*-algebra Q_2

## Endomorphisms and automorphisms of the 2-adic ring C*-algebra Q_2Add to your list(s) Download to your calendar using vCal - Stefano Rossi (Università degli Studi di Roma Tor Vergata; Università degli Studi di Roma Tor Vergata)
- Thursday 16 February 2017, 14:00-15:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. OAS - Operator algebras: subfactors and their applications The 2-adic ring C =1. By its very definition it contains a copy of the Cuntz algebra O_2. I'll start by discussing some nice properties of this inclusion, as they came to be pointed out in a recent joint work with V. Aiello and R. Conti. Among other things, the inclusion enjoys a kind of rigidity property, i.e., any endomorphism of the larger that restricts trivially to the smaller must be trivial itself. I'll also say a word or two about the extension 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 endomorphisms (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, including those fixing the diagonal D_2. Notably, the semigroup of the endomorphisms fixing U turns out to be a maximal abelian group isomorphic with the group of continuous functions from the one-dimensional torus to itself. Such an analysis, though, calls for some knowledge of the inner structure of Q_2. More precisely, it's vital to prove 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 working with N. Stammeier as well.This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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