A note to the unipotency of the identity component of the group of algebra automorphisms.
Kures̆, Miroslav (2007)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Kures̆, Miroslav (2007)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Marek Karaś, Jakub Zygadło (2012)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let d be any integer greater than or equal to 3. We show that the intersection of the set mdeg(Aut(ℂ³))∖ mdeg(Tame(ℂ³)) with {(d₁,d₂,d₃) ∈ (ℕ ₊)³: d = d₁ ≤ d₂≤ d₃} has infinitely many elements, where mdeg h = (deg h₁,...,deg hₙ) denotes the multidegree of a polynomial mapping h = (h₁,...,hₙ): ℂⁿ → ℂⁿ. In other words, we show that there are infinitely many wild multidegrees of the form (d,d₂,d₃), with fixed d ≥ 3 and d ≤ d₂ ≤ d₃, where a sequence (d₁,...,dₙ)∈ ℕ ⁿ is a wild multidegree...
Giovanni Cutolo (1992)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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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.
Cohn, P. (2002)
Serdica Mathematical Journal
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The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate...
Marek Karaś (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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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.
William F. Keigher, V. Ravi Srinivasan (2011)
Banach Center Publications
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In this article, we study solutions of linear differential equations using Hurwitz series. We first obtain explicit recursive expressions for solutions of such equations and study the group of differential automorphisms of the solutions. Moreover, we give explicit formulas that compute the group of differential automorphisms. We require neither that the underlying field be algebraically closed nor that the characteristic of the field be zero.
David Sherman (2009)
Studia Mathematica
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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...
Federico Menegazzo (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Richard Byrd, Justin Lloyd, Franklin Pederson, James Stepp (1984)
Fundamenta Mathematicae
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F. S. Cater, A. B. Thaheem (1996)
Rendiconti del Seminario Matematico della Università di Padova
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Jérémie Rostand (2003)
Studia Mathematica
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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...