C[subscript 2]-cofiniteness of the vertex algebra V[subscript L] [superscript +] and classification of irreducible modules of the vertex operator algebra V[subscript L] [superscript +]
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Title C[subscript 2]-cofiniteness of the vertex algebra V[subscript L] [superscript +] and classification of irreducible modules of the vertex operator algebra V[subscript L] [superscript +]
Creator Phichet Jitjankarn
Contributor Patanee Udomkavanich, Gaywalee Yamskulna
Publisher Chulalongkorn University
Publication Year 2552
Keyword Vertex operator algebras
Abstract The first part of this thesis is the study of the representation theory of vertex algebras V[subscript L] [superscript +] when L are nondegenerate even lattices that are not positive de nite. In particular, we show that such vertex algebras and their irreducible weak modules satisfy the so-called C[subscript 2]-co niteness condition. For the second part of this thesis, we study the representation theory of a vertex operator algebra V[subscript L] [superscript +]. Here L is a positive de nite even lattice of rank 2 and tau is an auto-morphism of V[subscript L] [superscript +]. We are able to classify some irreducible V[subscript L] [superscript +] -modules that are contained in irreducible V[subscript L] [superscript +] -modules. Furthermore, we construct and classify some tau-twisted modules of a vertex algebra M(1)[superscript +]. This vertex algebra is a vertex subalgebra of V[subscript L] [superscript +].
URL Website cuir.car.chula.ac.th
Chulalongkorn University

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