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University of Southern California

1. Warner, Harry Jared, IV. Springer isomorphisms and the variety of elementary subalgebras.

Degree: PhD, Mathematics, 2015, University of Southern California

Over a field of large enough characteristic, we use the canonical Springer isomorphism between the unipotent variety of a connected, reductive group and the nilpotent variety of the group's Lie algebra to study the projective variety of elementary subalgebras, as defined by Jon Carlson, Eric Friedlander, and Julia Pevtsova. When our structures are defined over finite fields, we relate certain computable information about elementary abelian subgroups of Chevalley groups with rational points and orbits of the variety of elementary subalgebras. We also construct the commuting variety of one-parameter subgroups which simultaneously generalizes the variety of elementary subalgebras and the variety of one-parameter subgroups, as defined by Andrei Suslin, Eric Friedlander, and Christopher Bendel. We employ Magma to make many computations and draw certain visualizations of the theory. Advisors/Committee Members: Friedlander, Eric M. (Committee Chair), Guralnick, Robert M. (Committee Member), Montgomery, M. Susan (Committee Member), Jonckheere, Edmond A. (Committee Member).

Subjects/Keywords: affine group schemes; representation theory; support varieties; Springer isomorphism; algebraic groups; elementary subalgebras; restricted Lie algebras; elementary Abelian subgroups

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Warner, Harry Jared, I. (2015). Springer isomorphisms and the variety of elementary subalgebras. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/541250/rec/6023

Chicago Manual of Style (16th Edition):

Warner, Harry Jared, IV. “Springer isomorphisms and the variety of elementary subalgebras.” 2015. Doctoral Dissertation, University of Southern California. Accessed September 20, 2020. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/541250/rec/6023.

MLA Handbook (7th Edition):

Warner, Harry Jared, IV. “Springer isomorphisms and the variety of elementary subalgebras.” 2015. Web. 20 Sep 2020.

Vancouver:

Warner, Harry Jared I. Springer isomorphisms and the variety of elementary subalgebras. [Internet] [Doctoral dissertation]. University of Southern California; 2015. [cited 2020 Sep 20]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/541250/rec/6023.

Council of Science Editors:

Warner, Harry Jared I. Springer isomorphisms and the variety of elementary subalgebras. [Doctoral Dissertation]. University of Southern California; 2015. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/541250/rec/6023

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