2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/190697We show that D-branes in the Euclidean $AdS_3$ can be naturally associated to the maximally isotropic subgroups of the Lu-Weinstein double of SU(2). This picture makes very transparent the residual loop group symmetry of the D-brane configurations and gives also immediately the D-branes shapes and the $σ$-model boundary conditions in the de Sitter T-dual of the $SL(2,C)/SU(2)$ WZW model.29 pages, LaTeX, references addedHigh Energy Physics - Theorytext