Vol. 78, No. 2, 1978

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On representing analytic groups with their automorphisms

G. Hochschild

Vol. 78 (1978), No. 2, 333–336

A real or complex Lie group is said to be faithfully representable if it has a faithful finite-dimensional analytic representation. Let G be a real or complex analytic group, and let A denote the group of all analytic automorphisms of G, endowed with its natural structure of a real or complex Lie group. The natural semidirect product G A is a real or complex Lie group, sometimes called the holomorph of G. We show that if G is faithfully representable and if the maximum nilpotent normal analytic subgroup of G is simply connected then G A is faithfully representable.

Mathematical Subject Classification 2000
Primary: 22E45
Received: 25 February 1978
Published: 1 October 1978
G. Hochschild