請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6286完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 程舜仁(S. J. Cheng) | |
| dc.contributor.author | Che-Sheng Su | en |
| dc.contributor.author | 蘇哲聖 | zh_TW |
| dc.date.accessioned | 2021-05-16T16:25:03Z | - |
| dc.date.available | 2013-07-03 | |
| dc.date.available | 2021-05-16T16:25:03Z | - |
| dc.date.copyright | 2013-07-03 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-06-10 | |
| dc.identifier.citation | Bibliography
[ATLAS] J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker and R.A. Wilson, ATLAS of finite groups. Clarendon Press, Oxford, 1985. [Co] J.H. Conway, A simple construction for the Fischer-Griess Monster group, Inventiones Mathematicae 79 (1985), 513–540. [DMZ] C. Y. Dong, G. Mason, and Y. Zhu, Discrete series of the Virasoro algebra and the Moonshine module, Proceedings of Symposia in Pure Mathematics 56 Part 2 (1994) 295-316. [DLMN] C. Dong, H. Li, G. Mason, and S.P. Norton, Associative subalgebras of Griess algebra and related topics. Proceedings of the Conference on the Monster and Lie algebra at the Ohio State University, May 1996, ed. by J. Ferrar and K. Harada, Walter de Gruyter, Berlin - New York, 1998. [FHL] I. Frenkel, Y. Z. Huang, and J. Lepowsky, On axiomatic approaches to vertex operator algebras and modules, Memoirs of the American Mathematical Society 104, 1993. [FLM] I. Frenkel, J. Lepowsky, and A. Meurman, Vertex operator algebras and the Monster, Academic Press, New York, 1988. [FZ] Igor B. Frenkel, and Y. C. Zhu, Vertex operator algebras associated to representations of affine and Virasoro algebras, Duke Mathematical Journal 66 (1992) 123-168. [GL] R.L. Griess, Jr. and C.H. Lam, Diagonal lattices and rootless EE8 pairs, J. Pure and Applied Algebra 216(2012), no. 1, 154-169. [Ho] G. Hohn, The group of symmetries of the shorter moonshine module, Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg 80 (2010), 275–283, arXiv:math/0210076. [HLY1] G. Hohn, C. H. Lam, and H. Yamauchi, McKay’s E7 observation on the Baby- monster, International Mathematics Research Notices (2012) Vol. 2012, 166-212; doi: 10.1093/imrn/rnr009. [HLY2] G. Hohn, C. H. Lam, and H. Yamauchi, McKay’s E6-observation on the largest Fischer group, Comm. Math. Phys., 310(2012), 329-365. [IPSS] A. A. Ivanov, D. V. Pasechnik, A. Seress, and S. Shpectorov, Majorana representations of the symmetric group of degree 4, Journal of Algebra 324 (2010) 2432-2463. [Kac] V. Kac, Vertex algebras for beginners, Second edition, University Lecture Series 10, American Mathematical Society, Providence, RI, 1998. [KMY] M. Kitazume, M. Miyamoto and H. Yamada, Ternary codes and vertex operator algebras. J. Algebra 223 (2000), 379–395. [Li] H. S. Li, Symmetric invariant bilinear forms on vertex operator algebras, Journal of Pure and Applied Algebra 96 (1994) 279-297. [LLY] C. H. Lam, N. Lam, H. Yamauchi, Extension of unitary Virasoro vertex operator algebra by a simple module, International Mathematics Research Notices11 (2003), 577-611. [LM] C.H. Lam and M. Miyamoto, Niemeier lattices, Coxeter elements, and McKay’s E8- observation on the Monster simple group, Internat. Math. Res. Notices Article ID 35967 (2006), 1–27. [LS] C. H. Lam, and C. S. Su, Griess algebras generated by 3 Ising vectors of central 2A-type, Journal of Algebra 374 (2013) 141-166. [LSh] C. H. Lam, and H. Shimakura, Ising vectors in the vertex operator algebra V + associated with the Leech lattice, International Mathematics Research Notices 2007 Art. ID rnm132, 21pp. [LYY1] C. H. Lam, H. Yamada, H. Yamauchi, Vertex operator algebras, extended E8 diagram, and McKay’s observation on the Monster simple group, Transactions of the American Mathematical Society 359 (2007) 4107-4123. [LYY2] C. H. Lam, H. Yamada, H. Yamauchi, McKay’s observation and vertex operator algebras generated by two conformal vectors of central charge 1/2, International Mathematics Re- search Papers 3 (2005), 117-181. [Ma] Atsushi Matsuo, 3-transposition groups of symplectic type and vertex operator algebras, Journal of the Mathematical Society of Japan 57 (2005) 639-649. [McK] J. McKay, Graphs, singularities, and finite groups, Proc. Symp. Pure Math., Vol. 37, Amer. Math. Soc., Providence, RI, 1980, pp. 183–186. 108 [Mi1] M. Miyamoto, Griess algebras and conformal vectors in vertex operator algebras, Journal of Algebra 179(1996) 523-548. [Mi2] M. Miyamoto, 3-state Potts model and automorphisms of vertex operator algebras of order 3. Journal of Algebra 239 (2001), 56-76. [Mi3] M. Miyamoto, Vertex operator algebras generated by two conformal vectors whose tau-involutions generate S3, Journal of Algebra 268 (2003), 653-671. [Mi4] M. Miyamoto, A new construction of the moonshine vertex operator algebra over the real number field, Annals of Mathematics 159 (2004) 535-596. [MeN] W. Meyer and W. Neutsch, Associative subalgebras of the Griess algebra. J. Algebra 158 (1993), 1–17. [Sa] Shinya Sakuma, 6-transposition property of ⌧-involutions of vertex operator algebras, Inter- national Mathematics Research Notices 2007, Article ID rnm 030, 19 pages. [SY] S. Sakuma and H. Yamauchi, Vertex operator algebra with two Miyamoto involutions generating S3, Journal of Algebra 267 (2003), 272-297. [Y] H. Yamauchi, 2A-orbifold construction and the baby-monster vertex operator superalgebra. J. Algebra 284 (2005), 645–668. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6286 | - |
| dc.description.abstract | In this dissertation, we study Griess algebras generated by Ising vectors. We consider two different cases. In the first case, we study Griess algebras generated by 3 Ising vectors with a common central 2A axial element. In the second case, we consider Griess algebras generated by two 3A-algebras with a common 3A axial element. In both cases, we classified all possible Griess algebras, up to isomorphism, and related them the McKay's E7 and E6 observations about the Baby Monster and the Fischer group. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-16T16:25:03Z (GMT). No. of bitstreams: 1 ntu-102-D97221001-1.pdf: 1626678 bytes, checksum: 86bce40f7c2510ff6f896948435eae65 (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | Chapter 1. Introduction 7
Chapter 2. Preliminary 11 2.1. Formal power series 11 2.2. Virasoro algebra 11 2.3. Formal definition of VOA 12 2.4. Module 14 2.5. Dual module 15 2.6. Morphism 16 2.7. Griess algebra 17 2.8. Virasoro VOA 18 2.9. Ising vectors 19 2.10. ⌧ -involution and '-involution 20 2.11. Eigenspace decomposition 21 2.12. Norton inequality 22 Chapter 3. Dihedral algebras and McKay’s observation 23 3.1. Lattice VOA 23 3.2. p2 times root lattices 29 3.3. Vp2R for a root lattice R 30 3.4. McKay’s observation 31 Chapter 4. Griess algebra generated by 2 Ising vectors 45 Chapter 5. Griess algebras generated by 3 Ising vectors of central 2A-type 53 5.1. Main theorem 54 5.2. Proof of the main theorem 56 Chapter 6. Griess algebras generated by two 3A-algebras with a common axis 81 6.1. An order 3 automorphism induced by W(4/5) 81 6.2. Main setting 83 6.3. The second main theorem 84 Bibliography 107 | |
| dc.language.iso | zh-TW | |
| dc.title | 由Ising向量生成的頂點算子代數及Griess代數 | zh_TW |
| dc.title | Vertex operator algebras and Griess algebras generated by Ising vectors | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 林正洪(C. H. Lam),陳榮凱(J. K. Chen),李白飛(P. H. Lee),林牛(N. Lam) | |
| dc.subject.keyword | 頂點算子代數, | zh_TW |
| dc.subject.keyword | vertex operator algebra,Griess algebra,Ising vector,Virasoro algebra, | en |
| dc.relation.page | 109 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2013-06-10 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-102-1.pdf | 1.59 MB | Adobe PDF | 檢視/開啟 |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。