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研究生:莊瑞麟
研究生(外文):Jui-LinChuang
論文名稱:Virasoro 頂點算子代數L(7/10,0)的擴充
論文名稱(外文):Extensions of tensor products of the unitary Virasoro vertex operator algebra L(7/10,0)
指導教授:林正洪林正洪引用關係
指導教授(外文):Ching-Hung Lam
學位類別:博士
校院名稱:國立成功大學
系所名稱:數學系應用數學碩博士班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:英文
論文頁數:76
中文關鍵詞:超級頂點算子代數密碼維拉宿代數
外文關鍵詞:SVOAcodeVirasoro algebra
相關次數:
  • 被引用被引用:0
  • 點閱點閱:90
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  • 下載下載:3
  • 收藏至我的研究室書目清單書目收藏:0
參考宮本教授的方法, 我們利用二進制的密碼, L(7/10,0)和L(7/10,0)所有不同構的不可約模來構照密碼超級頂點算子代數. 主要是分類這樣的頂點算子代數表現理論與其對應的不同構模. 另外我們還證明了怎樣的頂點算子代數會與我們所架構的密碼頂點代數同構.
Following the approach of [25], we construct a class of vertex operator (super) algebra WD using some binary code D and irreducible modules of the unitary Virasoro vertex operator algebra L( 7/10 ; 0). We also introduce a notion of induced modules and show that all irreducible WD-modules are induced modules. In addition, we study the fusion rules and show that certain irreducible WD modules are simple current modules.
1. Introduction 8
2. Basic definitions and preliminaries 12
2.1 (Super) vertex operator algebras and modules 13
2.2 Intertwining operators 17
2.3 Fusion algebra 18
3. Virasoro vertex operator algebra L(7/10,0) 21
3.1 Virasoro vectors of central charge 1/2 and 7/10 22
3.2 Casimir vectors and conformal design 25
3.3 Virasoro vector of σ-type 29
4. Lattice VOA and a super-extension of L(7/10,0) 34
4.1 The lattice VOA V_{√2A_2} 36
4.2 Some intertwining operators 40
5. Extensions of the VOA L(7/10,0)^{⊗n} 43
5.1 Construction of code SVOA 44
6. Irreducible WD-modules 48
6.1 Structure of W_D-modules 48
6.2 Notions of W_D-modules 51
6.3 Construction of W_D-modules 56

7. Some simple current modules and their application 63
7.1 Simple current super-extension of the W_D 63
7.2 Some simple current W_D-module 67
8. Uniqueness of simple SVOA 69
8.1 the T-condition for c =7/10 69
Bibliography 76
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