THESIS
2017
viii, 78 pages : illustrations ; 30 cm
Abstract
In this thesis, we study the VOA V
_{J,r} associated to a Hermitian type Jordan algebra J, and mainly discuss the case when J is of B type. The content of this thesis is divided into three parts. The first part consists of Chapter 1, Chapter 2, and Chapter 3. We give a brief account of the theory of vertex algebra. We also review the VOAs V̄
_{J,1}, V
_{J,r}, where J is a B type Jordan algebra. The second part is from Chapter 4 to Chapter 6. We discuss some further properties of the VOA V
_{J ,r}, where J is a B type Jordan algebra. We compute the correlation function of the fields associated to V
_{J,r}, and give explicit constructions of the simple quotients V̄
_{J,r} when r ∈ Z
_{≠0}, using dual pair type constructions. We also calculate the character formula for the simple quotients V̄
_{J,r}, r = -2n, n ≥ 1. The...[
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In this thesis, we study the VOA V
_{J,r} associated to a Hermitian type Jordan algebra J, and mainly discuss the case when J is of B type. The content of this thesis is divided into three parts. The first part consists of Chapter 1, Chapter 2, and Chapter 3. We give a brief account of the theory of vertex algebra. We also review the VOAs V̄
_{J,1}, V
_{J,r}, where J is a B type Jordan algebra. The second part is from Chapter 4 to Chapter 6. We discuss some further properties of the VOA V
_{J ,r}, where J is a B type Jordan algebra. We compute the correlation function of the fields associated to V
_{J,r}, and give explicit constructions of the simple quotients V̄
_{J,r} when r ∈ Z
_{≠0}, using dual pair type constructions. We also calculate the character formula for the simple quotients V̄
_{J,r}, r = -2n, n ≥ 1. The third part is Chapter 7. We
sketch the constructions of V
_{J,r} for all Hermitian type Jordan algebras J. We also propose some problems for future study.
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