Graduation Term
Spring 2025
Degree Name
Master of Science (MS)
Department
Department of Mathematics
Committee Chair
Gaywalee Yamskulna
Committee Member
Charlotte Ure
Abstract
In this thesis, we study how the higher-level Zhu algebras of a vertex algebra reflect the structure of associated simple Leibniz algebras. In particular, we construct a vertex algebra from a vertex algebroid containing the simple Lie algebra sl2 and analyze its higher level Zhu algebras. The irreducible modules of this vertex algebra were completely classified in [JY20b], but the structure of its indecomposable modules remains an open problem. Since modules for higher level Zhu algebras correspond to modules of vertex algebras, studying these algebras provides a method for understanding their broader representation theory.
Access Type
Thesis-Open Access
Recommended Citation
Soltermann, Christian, "On Higher Level Zhu Algebras of N-Graded Vertex Algebras Associated with Simple Leibniz Algebras That Contain sl2" (2025). Theses and Dissertations. 2080.
https://ir.library.illinoisstate.edu/etd/2080