The varieties of Heisenberg vertex operator algebras

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• 作者：YanJun Chu ; ZongZhu Lin
• 关键词：vertex operator algebra ; semi ; conformal vector ; variety
• 刊名：Science China Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：60
• 期：3
• 页码：379-400
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics;
• 出版者：Science China Press
• ISSN：1869-1862
• 卷排序：60

文摘

For a vertex operator algebra V with conformal vector ω, we consider a class of vertex operator subalgebras and their conformal vectors. They are called semi-conformal vertex operator subalgebras and semiconformal vectors of (V,ω), respectively, and were used to study duality theory of vertex operator algebras via coset constructions. Using these objects attached to (V, ω), we shall understand the structure of the vertex operator algebra (V, ω). At first, we define the set Sc(V, ω) of semi-conformal vectors of V, then we prove that Sc(V, ω) is an affine algebraic variety with a partial ordering and an involution map. Corresponding to each semi-conformal vector, there is a unique maximal semi-conformal vertex operator subalgebra containing it. The properties of these subalgebras are invariants of vertex operator algebras. As an example, we describe the corresponding varieties of semi-conformal vectors for Heisenberg vertex operator algebras. As an application, we give two characterizations of Heisenberg vertex operator algebras using the properties of these varieties.