Displaying similar documents to “On the automorphism group of a complex sphere.”

Tame Automorphisms of ℂ³ with Multidegree of the Form (p₁,p₂,d₃)

Marek Karaś (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

Let d₃ ≥ p₂ > p₁ ≥ 3 be integers such that p₁,p₂ are prime numbers. We show that the sequence (p₁,p₂,d₃) is the multidegree of some tame automorphism of ℂ³ if and only if d₃ ∈ p₁ℕ + p₂ℕ, i.e. if and only if d₃ is a linear combination of p₁ and p₂ with coefficients in ℕ.

On the automorphisms of the spectral unit ball

Jérémie Rostand (2003)

Studia Mathematica

Similarity:

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...

On the automorphism group of the countable dense circular order

J. K. Truss (2009)

Fundamenta Mathematicae

Similarity:

Let (C,R) be the countable dense circular ordering, and G its automorphism group. It is shown that certain properties of group elements are first order definable in G, and these results are used to reconstruct C inside G, and to demonstrate that its outer automorphism group has order 2. Similar statements hold for the completion C̅.