The automorphisms groups of symmetric algebras

Ernest Płonka

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CONTENTSIntroduction.................................................................................................................... 5Section 1. The group of weak automorphisms...................................................... 6Section 2. Weak automorphisms of finitely generated free algebras................ 9Section 3. Representation of groups as weak automorphism groups ofalgebras............................................................................................................................

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This mainly expository article is devoted to recent advances in the study of dynamical aspects of the Cuntz algebras 𝓞ₙ, n < ∞, via their automorphisms and, more generally, endomorphisms. A combinatorial description of permutative automorphisms of 𝓞ₙ in terms of labelled, rooted trees is presented. This in turn gives rise to an algebraic characterization of the restricted Weyl group of 𝓞ₙ. It is shown how this group is related to certain classical dynamical systems on the Cantor...

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