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Classification of certain genera of codes, lattices and vertex operator algebras

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Bibliographic Details
Title: Classification of certain genera of codes, lattices and vertex operator algebras
Authors: Junla, Nakorn
Publisher Information: Kansas State University
Collection: Kansas State University: K-State Research Exchange (K-REx)
Subject Terms: Vertex operator algebra genera, Code type lattice genera, Mathematics (0405)
Description: Doctor of Philosophy ; Department of Mathematics ; Gerald H. Höhn ; We classify the genera of doubly even binary codes, the genera of even lattices, and the genera of rational vertex operator algebras (VOAs) arising from the modular tensor categories (MTCs) of rank up to 4 and central charges up to 16. For the genera of even lattices, there are two types of the genera: code type genera and non code type genera. The number of the code type genera is finite. The genera of the lattices of rank larger than or equal to 17 are non code type. We apply the idea of a vector valued modular form and the representation of the modular group SL[subscript]2(Z) in [Bantay2007] to classify the genera of the VOAs arising from the MTCs of ranks up to 4 and central charges up to 16.
Document Type: doctoral or postdoctoral thesis
File Description: application/pdf
Language: English
Relation: http://hdl.handle.net/2097/18181
Availability: http://hdl.handle.net/2097/18181
Accession Number: edsbas.BFC51525
Database: BASE
Description
Abstract:Doctor of Philosophy ; Department of Mathematics ; Gerald H. Höhn ; We classify the genera of doubly even binary codes, the genera of even lattices, and the genera of rational vertex operator algebras (VOAs) arising from the modular tensor categories (MTCs) of rank up to 4 and central charges up to 16. For the genera of even lattices, there are two types of the genera: code type genera and non code type genera. The number of the code type genera is finite. The genera of the lattices of rank larger than or equal to 17 are non code type. We apply the idea of a vector valued modular form and the representation of the modular group SL[subscript]2(Z) in [Bantay2007] to classify the genera of the VOAs arising from the MTCs of ranks up to 4 and central charges up to 16.