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Dickson FINAL 4 30 2021 with cert.pdf (468.13 KB)

ETD Abstract Container

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An Introduction to Lie Theory and Applications

Dickson, Anthony J
http://rave.ohiolink.edu/etdc/view?acc_num=ysu1619868531483866

Abstract Details

2021, Master of Science in Mathematics, Youngstown State University, Department of Mathematics and Statistics.
This thesis goes over various topics of Lie theory and is meant as an introduction for those who have never studied the subject. This is accomplished by first reviewing necessary background material, including topics from linear algebra and topology (where no background knowledge is assumed), before proceeding to the main subject. We start by discussing the matrix Lie group before discussing what a Lie algebra is. We define a Lie algebra as a vector space with additional requirements before defining it again with relation to a Lie group. We then explore various properties and examples of this. Next, we turn to representation theory and how it can be applied to Lie theory, including the important subject of roots and weights. Finally we finish by briefly going over some connections Lie theory has with physics (no background physics knowledge is assumed of the reader). Overall, the main goal of this thesis is to be an accessible starting point for someone who has a strong background in linear and abstract algebra, but has never studied Lie theory.
Thomas Madsen, PhD (Advisor)
Tom Wakefield, PhD (Committee Member)
Michael Crescimanno, PhD (Committee Member)
84 p.
Mathematics; Theoretical Mathematics
Lie theory; Lie algebra; math physics

Recommended Citations

Citations

  • Dickson, A. J. (2021). An Introduction to Lie Theory and Applications [Master's thesis, Youngstown State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1619868531483866

    APA Style (7th edition)

  • Dickson, Anthony. An Introduction to Lie Theory and Applications. 2021. Youngstown State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ysu1619868531483866.

    MLA Style (8th edition)

  • Dickson, Anthony. "An Introduction to Lie Theory and Applications." Master's thesis, Youngstown State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1619868531483866

    Chicago Manual of Style (17th edition)

ysu1619868531483866
378
© 2021, all rights reserved.
This open access ETD is published by Youngstown State University and OhioLINK.