On a problem of Bjarni Jónsson concerning automorphisms of a general algebra

Ernest Płonka

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Notes on automorphisms of ultrapowers of II₁ factors

David Sherman (2009)

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In functional analysis, approximative properties of an object become precise in its ultrapower. We discuss this idea and its consequences for automorphisms of II₁ factors. Here are some sample results: (1) an automorphism is approximately inner if and only if its ultrapower is ℵ₀-locally inner; (2) the ultrapower of an outer automorphism is always outer; (3) for unital *-homomorphisms from a separable nuclear C*-algebra into an ultrapower of a II₁ factor, equality of the induced traces...

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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...

Automorphisms of ${\overset{ˇ}{U}}_{q} (𝔟^{+})$ . (Automorphismes de ${\overset{ˇ}{U}}_{q} (𝔟^{+})$ .)

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A note on central automorphisms of groups

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A characterization of central automorphisms of groups is given. As an application, we obtain a new proof of the centrality of power automorphisms.

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On the automorphisms of the spectral unit ball

Jérémie Rostand (2003)

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Let Ω be the spectral unit ball of Mₙ(ℂ), that is, the set of n × n matrices with spectral radius less than 1. We are interested in classifying the automorphisms of Ω. We know that it is enough to consider the normalized automorphisms of Ω, that is, the automorphisms F satisfying F(0) = 0 and F'(0) = I, where I is the identity map on Mₙ(ℂ). The known normalized automorphisms are conjugations. Is every normalized automorphism a conjugation? We show that locally, in a neighborhood of a...