Семинар за логику, 15. новембар 2019.

Наредни састанак Семинара биће одржан у петак, 15. новембра 2019. у сали 301f Математичког института САНУ са почетком у 14:15. У питању је заједнички састанак са Одељењем за математику.

Предавач: Saeed Ghasemi, Institute of Mathematics CAS, Prague

Наслов предавања: STRONGLY SELF-ABSORBING C*-ALGEBRAS AND FRAISSE LIMITS

Апстракт:
A unital separable C*-algebra (other than the C*-algebra of all complex numbers) is strongly self absorbing if it is isomorphic to its (minimal) tensor product with itself, in a "strong" sense. Strongly self-absorbing C*-algebras play a crucial role in Elliott's classification program of separable nuclear C*-algebras by K-theoretic data. Among them, the Jiang-Su algebra Z has a special place and, to this date, the classification of separable, simple, unital, nuclear C*-algebras that tensorially absorb Z and satisfy the UCT has been the most remarkable achievement of the classification program. In their original paper from 1999, Jiang and Su already prove that Z is strongly self-absorbing. However, their proof uses heavy tools from classification, such as KK-theory and it is quite difficult. We give a self contained, rather elementary and direct proof for the fact that Z is strongly self-absorbing. This is done by establishing a general connection between the strongly self-absorbing C*-algebras and the Fraisse limits of categories of C*-algebras that are sufficiently closed under tensor products. It was previously known that Z can be realized as the "Fraisse limit" of a certain category of C*-algebras and embeddings consisting of its building blocks, i.e. the prime dimension-drop algebras.


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