Lie algebra decompositions with applications to quantum dynamics
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Lie group decompositions are useful tools in the analysis and control of quantum systems. Several decompositions proposed in the literature are based on a recursive procedure that systematically uses the Cartan decomposition theorem. In this dissertation, we establish a link between Lie algebra gradings and recursive Lie algebra decompositions, and then we formulate a general scheme to generate Lie group decompositions. This scheme contains some procedures previously proposed as special cases and gives a virtually unbounded number of alternatives to factor elements of a Lie group.