# 臺灣博碩士論文加值系統

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 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 82. Basic definitions and preliminaries 12 2.1 (Super) vertex operator algebras and modules 13 2.2 Intertwining operators 17 2.3 Fusion algebra 183. 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 294. 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 405. Extensions of the VOA L(7/10,0)^{⊗n} 43 5.1 Construction of code SVOA 446. 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 567. 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 678. Uniqueness of simple SVOA 69 8.1 the T-condition for c =7/10 69 Bibliography 76
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Studies in groups, nonassociative algebras and vertexoperator algbras. Vertex Operator Algebras in Mathematics and Physics (Toronto,2000), pp. 71ï£¡V88, Fields Ins. Commun., 39, Amer. Math. Soc., Providence, 2003.[22] K. Harada and M.-L. Lang,modular forms associated with the Monster module in TheMonster and Lie algebras (Columbus, Ohio, 1996), Ohio State Univ. Math. Res. Inst.Publ. 7, de Gruyter, Berlin, 1998, 59-83.[23] G. Höhn, Conformal designs based on vertex operator algebras, Adv.Math. 217 (2008),2301-2335.[24] G. Höhn, Ching Hung Lam, Hiroshi Yamauchi, McKay’s observations on the BabyMonster, Inter. Math. Res. Not., 2012(2012), 166-212.[25] G. Höhn, Ching Hung Lam, Hiroshi Yamauchi, McKay’s E7 and E6 observations onthe Babymonster and the largest Fischer group, Inter. Math Res. notice. 2011.[26] Y.-Z. Huang and J. Lopowsky, A theory of the tensor products for module categoriesfor a vertex operator algebra, III, J. Pure Appl. Algebra. 100 (1995), 141-171.[27] Y.-Z. Huang, Differential equations and intertwining operators, Comm. Contemp.Math. 7 (2005), 275-299.[28] G. Kac and A. K. Raina, Bombay lectures on highest weight representations of infinitedimensional Lie algebras. World Scientific Publishing Co Pte Ltd, 1988[29] M. Kitazume, M. Miyamoto and H. Yamada, Ternary codes and vertex operatoralgebras, J. Algebra, 223 (2000), 379-395.[30] C.H Lam and H. Yamada, Z2 Z2-codes and vertex operator algebras, J. Algebra224 (2000), 268-291.[31] C.H Lam, Some twisted modules for framed vertex operator algebras, J. Algebra, 231(2000), 331-341.h. Res. Inst. Publ. 7, de Gruyter, Berlin, 1998,[32] C.H Lam, N. Lam and H. Yamauchi, Extension of unitary Virasoro vertex operatoralgebra by a simple module. Internat. Math. Res. Notices 11 (2003), 577-611.[33] C.H Lam and H.Yamauchi, On the structure of the framed vertex operator algebrasand their pointwise frame stabilizers, Comm. math. Physics 277(2008), no. 1, 237-285.[34] C.H. Lam, H. Yamada and H. Yamauchi, McKay’s observation and vertex operatoralgebras generated by two conformal vectors of central charge 1/2. Internat. Math. Res.Papers 3 (2005), 117–181.[35] H. Li: Symmetric invariant bilinear forms on vertex operator algebras, J. Pure Appl.Algebra 96 (1994) 279-297.[36] H. Li, Local systems of vertex operators, vertex superalgebras and modules, J. PureAppl. Algebra, 109(1996), 143-195.[37] H. Li, Local systems of twisted vertex operators, vertex operator superalgebras andtwisted modules, in Moonshine, the Monster, and Related Topics (South Hadley, MA,1994), Editors C. Dong and G. Mason, Contemporary Mathematics, Vol. 193, AmericanMathematical Society, Providence, RI, 1996, 203-236[38] A. Matsuo, Norton’s trace formula for the Griess algebra of a vertex operator algebrawith large symmetry, Commun.Math.Phys. 224 (2001), 565-591.[39] M. Miyamoto, Griess algebras and conformal vectors in vertex operator algebras, J.Algebra 179(1996), 523-548.[40] M. 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Yamauchi, A theory of simple current extensions of vertex operator algebrasand applications to the moonshine vertex operator algebra, Ph.D. thesis, University ofTsukuba, 2004.; available on the author’s web site: http://www.ms.u-tokyo.ac.jp/ yamauchi
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