Date of Award

1-1-2018

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (ii, xvii, 127 pages) : illustrations.

Dissertation/Thesis Chair

Antun Milas

Committee Members

Christian Lenart, Changlong Zhong

Keywords

Vertex Algebras, Vertex operator algebras, Calculus of tensors, Modules (Algebra)

Subject Categories

Physical Sciences and Mathematics

Abstract

We consider the geometric foundations of certain vertex algebras and their modules according to the formalism of Harish-Chandra Geometry that we develop in conjunction with Formal Geometry. Our main result is that we introduce an extension of the torsor of formal coordinates whereby a sheaf of pro-coherent modules is obtained over an affine scheme that corresponds to a certain vertex algebra. As a corollary of this result, we obtain a similar sheaf of pro-coherent modules corresponding to certain representations of the aforementioned vertex algebra.

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