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Solid state physics provides a rather new application area for quantum control. Yet, the high dimensional state spaces in this field require a thorough analysis of the underlying Lie algebraic structures for developing efficient control strategies. In this paper, we focus a one-dimensional chain of quantum dots described by the Hubbard model. The model plays an extremely important role in solid state physics since it is the simplest model which explicitly takes into account the interplayfatcat:grhq77tfdzhlznipnzfud63q4m