Variations and generalizations of preprojective algebras
File(s)
Author(s)
Kaplan, Daniel
Type
Thesis or dissertation
Abstract
The preprojective algebra, defined by Gelfand and Ponomarev, is the algebraic precursor to the study of Nakajima quiver varieties, which are pervasive in geometric representation theory. Examples of such varieties include flag varieties (for the type A quivers) and the Hilbert schemes of points in the plane (for the Jordan quiver.) In this thesis, we take the algebra as the fundamental object of study. We produce interesting flat degenerations of the preprojective algebra, in the direction of Geiß, Leclerc, and Schröer following de Thanhoffer de Völcsey and Presotto. Additionally, we study a multiplicative analog of the preprojective algebra, and prove that a large class of such algebras are 2-Calabi-Yau.
Version
Open Access
Date Issued
2019-06
Date Awarded
2020-01
Copyright Statement
Creative Commons Attribution NonCommercial No Derivatives Licence
Advisor
Schedler, Travis
Sponsor
Imperial College London
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)