Non-abelian axial-vector duality: a geometric description

We give a geometric characterization of the quasi axial-vector (Kiritsis-Obers) target space duality in the spirit of the bi-algebra (Klimčik-Ševera) approach. We show that the σ-models constructed by taking quotients have non-abelian chiral currents that obey “non-commutative conservation laws” and provide the criterion for a σ-model to have a dual using the axial-vector procedure.