On the automorphisms of the spectral unit ball

• Autorzy: Jérémie Rostand
• Języki publikacji: EN

Abstrakty

EN

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 matrix with distinct eigenvalues, the answer is yes. We also prove that a normalized automorphism of Ω is a conjugation almost everywhere on Ω.

Kategorie tematyczne

• 32A07: Special domains (Reinhardt, Hartogs, circular, tube)
• 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions
• 32M05: Complex Lie groups, automorphism groups acting on complex spaces
• 15A18: Eigenvalues, singular values, and eigenvectors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 155
• Numer: 3
• Strony: 207-230

Daty

wydano

2003

Twórcy

autor

Jérémie Rostand

• Département de mathématiques et statistique, Université Laval, Québec, Canada G1K 7P4

Identyfikatory

DOI

10.4064/sm155-3-2