TOPOLOGICAL CURRENT-ALGEBRAS IN 2 DIMENSIONS

Two-dimensional topological field theories possessing a non-abelian cu rrent symmetry are constructed. The topological conformal algebra of t hese models is analysed. It differs from the one obtained by twisting the N=2 superconformal models and contains generators of dimensions 1, 2 and 3 that close a linear algebra. Our construction can be carried out with one and two bosonic currents and the resulting theories can b e interpreted as topological sigma models for group manifolds.