We study the transport properties of three quantum wires (with possibly different interaction strength), connected through a Y-junction, within the scattering state formalism. We first formulate the problem in current algebra language and focus on the case of a symmetric setup, for which the scattering matrix and the matrix of conductances is parametrized by two variables. For these we derive coupled RG equations, performing a ladder summation up to infinite order in the interaction. The fixed point structure and the implicit solution of these equations is presented. We show that higher order terms beyond the ladder approximation do not change the scaling behavior near the fixed points. For sufficiently strong attractive interaction a new fixed point with unusual properties is found.