Off-campus UMass Amherst users: To download campus access dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
Dissertations that have an embargo placed on them will not be available to anyone until the embargo expires.
Author ORCID Identifier
N/A
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2017
Month Degree Awarded
September
First Advisor
Eric Sommers
Subject Categories
Algebra
Abstract
This thesis investigates minimal generating sets of ideals defining certain nilpotent varieties in simple complex Lie algebras. A minimal generating set of invariants for the whole nilpotent cone is known due to Kostant. Broer determined a minimal generating set for the subregular nilpotent variety in all simple Lie algebra types. I extend Broer's results to two families of nilpotent varieties, valid in any simple Lie algebra, that include the nilpotent cone, the subregular case, and usually more. In the first part of my thesis I describe a minimal generating set for the ideal of each of these varieties in the coordinate ring of the Lie algebra. My goal in the second part is to describe which images of generators remain necessary when the variety is intersected with a Slodowy slice to a lower orbit and which become redundant, information that can be used to give new proofs of the singularities of minimal degenerations of nilpotent varieties.
DOI
https://doi.org/10.7275/10665216.0
Recommended Citation
Johnson, Benjamin, "Equations For Nilpotent Varieties and Their Intersections With Slodowy Slices" (2017). Doctoral Dissertations. 1100.
https://doi.org/10.7275/10665216.0
https://scholarworks.umass.edu/dissertations_2/1100