  Generalized current algebras introduced by Alekseev and Strobl in two
dimensions are reconstructed by a graded manifold and a graded Poisson
brackets. We generalize their current algebras to higher dimensions. QP
manifolds provide the unified structures of current algebras in any dimension.
Current algebras give rise to structures of Leibniz/Loday algebroids, which are
characterized by QP structures. Especially, in three dimensions, a current
algebra has a structure of a Lie algebroid up to homotopy introduced by Uchino
and one of the authors which has a bracket of a generalization of the
Courant-Dorfman bracket. Anomaly cancellation conditions are reinterpreted as
generalizations of the Dirac structure.
