"On Higher Level Zhu Algebras of N-Graded Vertex Algebras Associated wi" by Christian Soltermann

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

Included in

Algebra Commons

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