Degree Type

Honors Capstone Project

Date of Submission

Spring 5-1-2018

Capstone Advisor

Mark Kleiner

Honors Reader

Steven Diaz

Capstone Major

Mathematics

Capstone College

Arts and Science

Audio/Visual Component

no

Capstone Prize Winner

no

Won Capstone Funding

no

Honors Categories

Sciences and Engineering

Subject Categories

Mathematics | Other Mathematics | Physical Sciences and Mathematics

Abstract

The paper "Coxeter Functors and Gabriel's Theorem" written by I.N. Bernstein, I.M. Gel'fand, and V.A. Ponomarev explores the concept of reflection functors. A thorough proof of several results used by Bernstein et al in their paper is presented. The focus is on the category of representations and reflection functors, both negative and positive. The quadratic form is the bridge between the results on quivers and the techniques of Lie algebras. The Dynkin diagrams mentioned in Gabriel's Theorem are discussed.

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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