On roots of the automorphism group of a circular domain in $ℂ^n$

Jan M. Myszewski

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Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball $B_{𝔄}$ in a J*-algebra $𝔄$ of operators. Let $𝔉$ be the family of all collectively compact subsets W contained in $B_{𝔄}$ . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family $𝔉$ is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when $𝔄$ is a Cartan factor.

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2010 Mathematics Subject Classification: Primary 17B70, secondary 17B40, 16W50. Given a grading Γ : L ⨁ = g ∈ G L g on a nonassociative algebra L by an abelian group G, we have two subgroups of Aut(L): the automorphisms that stabilize each component L g (as a subspace) and the automorphisms that permute the components. By the Weyl group of Γ we mean the quotient of the latter subgroup by the former. In the case of a Cartan decomposition of a semisimple complex Lie algebra,...

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Displaying similar documents to “On roots of the automorphism group of a circular domain in ℂ n ”

Displaying similar documents to “On roots of the automorphism group of a circular domain in $ℂ^{n}$ ”