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We evaluate the ground state degeneracy of noncommutative Chern-Simons modelson the two-torus, a quantity that is interpreted as the "topological order" ofassociated phases of Hall fluids. We define the noncommutative theory viaT-duality from an ordinary Chern-Simons model with non-abelian 't Hooftmagnetic fluxes. Motivated by this T-duality, we propose a discrete family ofnoncommutative, non-abelian fluid models, arising as a natural generalizationof the standard noncommutative Chern-Simons effective models. We compute thetopological order for these universality classes, and comment on their possiblemicroscopic interpretation.

A note on the topological order of noncommutative Hall fluids