Degree Type

Dissertation

Date of Award

2008

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Domenico D'Alessandro

Second Advisor

Jonathan D. H. Smith

Third Advisor

Sung-Yell Song

Abstract

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.

DOI

https://doi.org/10.31274/rtd-180813-16930

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Mehmet Daǧlı

Language

en

Proquest ID

AAI3316246

OCLC Number

271225585

ISBN

9780549688952

File Format

application/pdf

File Size

78 pages

Included in

Mathematics Commons

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