Mathieu-Zhao Subspaces of Vertex Algebras

Author

Matthew Speck, Illinois State UniversityFollow

Date of Award

4-10-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Department of Mathematics

First Advisor

Gaywalee Yamskulna

Abstract

A Mathieu-Zhao subspace is a generalization of an ideal of an associative ring-algebra, A, first formalized in 2010. A vertex algebra is an algebraic structure first developed in conjunction with string theory in the 1960s and later axiomatized by mathematicians in the 1990s. We formally introduce the definition of a Mathieu-Zhao subspace, M, of a vertex algebra, V. Building on natural connections to associative algebras, we classify an infinite set of non-trivial, non-ideal Mathieu-Zhao subspaces for simple and general vertex algebras by group action eigenspace decomposition. Finally, we state the locally nilpotent epsilon-derivation (LNED) conjecture for vertex algebras.

Comments

Imported from ProQuest Speck_ilstu_0092N_11213.pdf

Recommended Citation

Speck, Matthew, "Mathieu-Zhao Subspaces of Vertex Algebras" (2018). Theses and Dissertations. 1030.
https://ir.library.illinoisstate.edu/etd/1030

DOI

http://doi.org/10.30707/ETD2019.Speck.M

Page Count

37