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Abstract
The aim of this paper is to introduce a notion of quantum groupoid, non-commutative analogue of Lie groupoids. This notion generalizes simultaneously the notion of a Hopf bigebroid [Mal] (corresponding to a quantum groupoid with commutative space of units) and the notion of a braided quantum group of Majid [Maj]. The commutativity hypothesis of the base in [Mal] is no more necessary and a construction of L. Vainerman [V] enters in this frame.