Date of Award

5-1-2021

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (viii, 147 pages) : illustrations.

Dissertation/Thesis Chair

Antun Milas

Committee Members

Cristian Lenart

Keywords

Superalgebras, Vertex operator algebras, Homology theory

Subject Categories

Physical Sciences and Mathematics

Abstract

\begin{center}{\large \textbf{Part 1.}}\\ \vspace*{0.1cm} \end{center} We generalize the notion of "quasi-lisse" vertex algebras to the super case. The modularity of quasi-lisse vertex superalgebra (twisted)modules is discussed. We study several families of vertex operator superalgebras from an arc (super)space point of view. We provide new examples of vertex algebras which are "chiral-quatizations" of their $C_{2}$-algebras $R_V$. Our examples come from certain $N=1$ superconformal vertex algebras, Feigin-Stoyanovsky principal subspaces, Feigin-Stoyanovsky type subspaces, graph vertex algebras $W_{\Gamma}$, and extended Virasoro vertex algebras. We also give some counterexamples to the chiral-quatizations property. For principal subspaces, their characters are closely related to $q$-series identities. In particular, we obtain new fermionic character formulas for level one $A$-type principal subspaces.

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