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Aims. We aim to study the geometry and kinematics of the disk around the Bestar $\alpha$ Arae as a function of wavelength, especially across theBr$\gamma$ emission line. The main purpose of this paper is to answer thequestion about the nature of the disk rotation around Be stars. Methods. We usethe VLTI/AMBER instrument operating in the K band which provides a gain by afactor 5 in spatial resolution compared to previous VLTI/MIDI observations.Moreover, it is possible to combine the high angular resolution provided withthe (medium) spectral resolution of AMBER to study the kinematics of the innerpart of the disk and to infer its rotation law. Results. We obtain for thefirst time the direct evidence that the disk is in keplerian rotation,answering a question that occurs since the discovery of the first Be star$\gamma$ Cas by father Secchi in 1866. We also present the global geometry ofthe disk showing that it is compatible with a thin disk + polar enhanced windsmodeled with the SIMECA code. We found that the disk around $\alpha$ Arae iscompatible with a dense equatorial matter confined in the central regionwhereas a polar wind is contributing along the rotational axis of the centralstar. Between these two regions the density must be low enough to reproduce thelarge visibility modulus (small extension) obtained for two of the four VLTIbaselines. Moreover, we obtain that $\alpha$ Arae is rotating very close to itscritical rotation. This scenario is also compatible with the previous MIDImeasurements.Comment: 15 page

First direct detection of a Keplerian rotating disk around the Be star $\mathsf{\alpha}$ Arae using AMBER/VLTI