Algebraic approach to anomalous sigma models

Anomalous σ-models in 1+1 and 1+3 dimensions are analysed using purely algebraic methods. We find, in the 1+1 dimensional example, a current algebra containing an arbitrary parameter which is compatible with the Wess-Zumino anomaly and anon-vanishing curvature. The consistency of the algebra is checked by means of a consistency condition and the Jacobi identity. In the 1+3 dimensional case, however, the conventional (anomalous) current algebra with a vanishing curvature is reproduced.