Date of Award
Doctor of Philosophy
Jonathan D. H. Smith
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.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Daǧlı, Mehmet, "Lie algebra decompositions with applications to quantum dynamics" (2008). Retrospective Theses and Dissertations. 15721.