Extended solutions in the noncommutative sigma-model

The notion of extended solution plays a key role in Uhlenbeck's approach to the description of harmonic maps from the two-dimensional sphere to the unitary group. In this talk we transfer this notion to the case of noncommutative sigma-model (a quantized analogue of harmonic spheres in the unitary group) and use it to establish that the minimal uniton number of a diagonal solution is equal to the canonical rank of this solution.