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The intergration of a Lie algebra interpretation

par Tits, Jacques ;Waelbroeck, Lucien
Référence Pacific journal of mathematics, 26, 3, page (595-600)
Publication Publié, 1968

Article révisé par les pairs

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Résumé :

Let u: G —> A be a differentiable representation of a Lie group into a 6-algebra. The differential u0 = du, of u at the neutral element e of G is a representation of the Lie algebra 9 of G into A. Because a Lie group is locally the union of one-parameter subgroups and since the infinitesimal generator of a differentiable (multiplicative) sub-semi-group of A determines this sub-semi-group, the representation u0 determines u if G is connected. We shall be concerned wi h the converse: given a representation u0 of o, when can it be obtained by differentiating a representation u of G? We shall assume G connected and simply connected, which means that we are only interested in the local aspect of the problem.