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# 林正洪

 Dr. Lam's research interest is on the structural and representation theory of vertex operator algebras and their applications to the theory of sporadic simple groups. In particular, he is interested in a special vertex operator algebra called Moonshine vertex operator algebra whose full automorphism group is the Monster simple group. Email : chlam AT math.sinica.edu.tw Phone:+886 2 2368-5999 ext. 705 Fax: +886 2 2368-9771

### 著作目錄 :

 1 (with Xingjun Lin) A Holomorphic vertex operator algebra of central charge 24 with weight one Lie algebra $F_{4,6}A_{2,2}$, preprint (2017) 2 (with Hsian-Yang Chen, Hiroki Shimakura) $\mathbb{Z}_3$-orbifold construction of the Moonshine vertex operator algebra and some maximal 3-local subgroups of the Monster, Mathematische Zeitschrift (2017) 3 (with Hiroki Shimakura) Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras, Preprint (2017) 4 (with Kazuya Kawasetsu, Xingjun Lin) $\mathbb{Z}_2$-orbifold construction associated with $(−1)$-isometry and uniqueness of holomorphic vertex operator algebras of central charge 24, Preprint (2017) 5 (with H. Shimakura) A holomorphic vertex operator algebras of central charge 24 whose weight one Lie algebra has type $A_{6,7}$, Letters in Mathematical Physics , 106(2016), 1575-1585 6 (with Hiroshi Yamauchi) The Conway-Miyamoto correspondences for the Fischer 3-transposition groups, preprint (2017) 7 (with Hiroshi Yamauchi) 3-dimensional Griess algebras and Miyamoto involutions, preprint (2017) 8 (with H.Y. Chen) Quantum dimensions and fusion rules of the VOA $V_{L_{C\times D}}^\tau$, Journal of Algebra , 459(2016-08), 309-349 9 (with H. Shimakura) Orbifold construction of holomorphic vertex operator algebras associated to inner automorphisms, Communications in Mathematical Physics , 342(2016-03), no. 3, 803-841 10 (with K. Harada) 'Inverses' of Virasoro operators, Communications in Algebra , 23(1995), no. 12, 4405-4413 11 Construction of vertex operator algebras form commutative associative algebras, Communications in Algebra , 24(1996), no. 14, 4439-4460 12 On VOA associated with special Jordan algebras, Communications in Algebra , 27(1999), no. 4, 1665-1681 13 Twisted repesentations of code vertex operator algebras, Journal of Algebra , 217(1999), no. 7, 275-299 14 Code vertex operator algebras under coordinates change, Communications in Algebra , 27(1999), no. 9, 4587-4605 15 (with C. Dong,and H. Yamada) Decomposition of the vertex operator algebra $V_{\sqrt{2}A_3}$, Journal of Algebra , 222(1999), 500-510 16 (with H. Yamada) $\mathbb{Z}_2\times \mathbb{Z}_2$ codes and vertex operator algebras, Journal of Algebra , 224(2000), 268-291 17 (with K.Kitazume, and H. Yamada) Decomposition of the Moonshine vertex operator algebra as Virasoro modules, Journal of Algebra , 226(2000), 893-919 18 Some twisted modules for framed vertex operator algebras, Journal of Algebra , 231(2000), 331-341 19 Representations of ternary code vertex operator algebras, Communications in Algebra , 29(2001), no. 3, 951-971 20 Fusion rules for Hamming code vertex operator algebra, Communications in Algebra , 29(2001), no. 5, 2125-2145 21 (with C. Dong,and H. Yamada) Decomposition of the vertex operator algebra $V_{\sqrt{2}D_n}$, Communications in Contemporary Mathematics , 3(2001), no. 1, 137-151 22 Induced modules for orbifold vertex operator algebras, Journal of Mathematical Society of Japan , 53(2001), no. 3, 541-557 23 (with M. Kitazume, and H. Yamada) A class of vertex operator algebras constructed from $\mathbb{Z}_8$-codes, Journal of Algebra (2001), 338-359 24 (with M. Kitazume, and H. Yamada) Moonshine vertex operator algebra as L(1/2,0) × L(7/10,0) × L(4/5,0) × L(1,0) -modules, Journal of Pure and Applied Algebra , 173(2002), no. 1, 15-48 25 (with M. Kitazume, and H. Yamada) 3-state Potts model, Moonshine vertex operator algebra and 3A-elements of the Monster group, International Mathematics Research Notices , 23(2003), 1269-1303 26 (with N. Lam, and H. Yamauchi) Extension of unitary Virasoro vertex operator algebra by a simple module, International Mathematics Research Notices , 11(2003), 577-611 27 (with H. Yamada) $\mathbb{Z}_3$-twisted representations of lattice vertex operator algebras, Communications in Algebra , 31(2003), no. 6, 3001-3020 28 (with Yamada H) Tricritical 3-state Potts model and vertex operator algebras constructed from ternary codes, Communications in Algebra , 32(2004), no. 11, 4197-4219 29 (with H. Yamada) Decomposition of the lattice vertex operator algebra $V_{\sqrt{2}A_{\ell}}$, Journal of Algebra , 272(2004), no. 2, 614-624 30 (with C. Dong, K. Tanabe, H. Yamada, and K. Yokoyama) $\mathbb{Z}_3$ symmetry and $W_3$ algebra in lattice vertex operator algebras, Pacific Journal of Mathematics , 215(2004), no. 5, 245-296 31 (with H. Yamada, and H. Yamauchi) McKay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2, Intern. Math. Res. Paper (2005), no. 3, 117-181 32 (with T. S. Chen) Extension of the tensor product of unitary Virasoro vertex operator algebras, Communications in Algebras , 35(2007), no. 8, 2487-2505 33 (with M. Miyamoto) Niemeier Lattices, Coxeter elements and McKay's E8 observation on the Monster simple group, Intern. Math. Res. Notices (2006), 0-0 34 (with H. Yamauchi) A characterization of the moonshine vertex operator algebra by means of Virasoro frames, Intern. Math. Res. Notices , 2007(2007), 0-0 35 (with C. Dong, R. L. Griess) Uniqueness results of Frenkel–Lepowsky -Meurman's moonshine vertex operator algebra, American Journal of Mathematics , 129(2007), no. 2, 583-609 36 (with H. Yamada and H. Yamauchi) Vertex operator algebra, extended E8 diagram and McKay’s observation on the Monster simple group, Transactions of American Mathematical Society , 359(2007), no. 9, 4107-4123 37 (with S. Sakuma and H. Yamauchi) Ising vectors and automorphism groups of commutant subalgebras related to root systems, Mathematische Zeitschrift , 255(2007), no. 3, 597-626 38 (with H. Shimakura) Ising vectors in the vertex operator algebra $V_{\Lambda}^+$ associated with the Leech lattice Λ, Intern. Math. Res. , 2007(2007), 0-0 39 (with H. Yamauchi) On the structure of framed vertex operator algebras and their pointwise frame stabilizers, Commun. Math. Phys. , 277(2008), no. 1, 237-285 40 (with R.L. Griess Jr.) Rootless pairs of EE8-lattices, Electronic Research Announcements in Mathematical Sciences , 15(2008), 52-61 41 (with C. Dong,and H. Yamada) W-algebras in lattice vertex operator algebras, in Lie Theory and Its Applications in Physics VII, ed. by H.-D. Doebner and V. K. Dobrev, Proc. of the VII International Workshop, Varna, Bulgaria , 2007(2008), no. 35, 25-35 42 (with S. Sakuma) On a class of vertex operator algebras having a faithful $S_{n+1}$-action, Taiwanese J. Math , 12(2008), no. 9, 2465-2488 43 (with H. Shimakura) Frame Stabilizers for Framed Vertex Operator Algebras Associated to Lattices Having 4-Frames, Int. Math. Res. Notices , 2009(2009), 4547-4577 44 (with C. Dong,and H. Yamada) W-algebras related to parafermion algebras, J. Algebra , 332(2009), 2236-2043 45 (with C. Dong, Q. Wang and H. Yamada) The structure of parafermion vertex operator algebras, J. Algebra , 323(2010), no. 2, 371-381 46 (with R.L. Griess Jr.) Dihedral groups and Sums of $EE_8$-lattices, Pure and applied mathematics quarterly , 7(2011), no. 3, 621-743 47 On the constructions of holomorphic vertex operator algebras of central charge 24, Comm. Math. Phys. , 305(2011), no. 1, 153-198 48 (with R. L. Griess) A moonshine path from $E_8$ to the Monster, J. Pure and Applied Algebra , 215(2011), 927-948 49 (with Robert L. Griess Jr.) A moonshine path for $5A$ and associated lattices of ranks 8 and 16, J. Algebra , 331(2011), 338-361 50 (with Gerald Hoehn; Hiroshi Yamauchi) McKay's $E_7$ observations on the Baby Monster, Inter. Math. Res. Not. , 2012(2012), 166-212 51 (with R.L. Griess, Jr.) Diagonal lattices and rootless $EE_8$ pairs, J. Pure and Applied Algebra , 216(2012), no. 1, 154-169 52 (with G. Hoehn, H. Yamauchi) McKay's $E_6$ observation on the largest Fischer group, Comm. Math. Phys. , 310(2012), 329-365 53 (with Masaaki Harada; Akihiro Munemasa) Residue codes of extremal Type II $\mathbb{Z}_4$-codes and the moonshine vertex operator algebra, Math. Z. , 274(2013), no. 1, 685-700 54 (with H. Shimakura) Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24, Proceedings of the London Mathematical Society , 104(2012), no. 3, 540-576(doi: 10.1112/plms/pdr041) 55 (with Robert L.~Griess Jr.) A new existence proof of the Monster by VOA theory, Michigan Mathematical Journal , 61(2012), 555-573 56 (with C.S. Su) Griess algebras generated by 3 Ising vectors of central 2A-type, J. algebra , 374(2013), 141-166 57 (with R.L. Griess) Moonshine paths for $3A$ and $6A$ nodes of the extended $E_8$-diagram, J. Algebra , 379(2013), 85-112 58 (with H.Y. Chen) Coset Construction of $\mathbb{Z}/3$ orbifold vertex operator algebra $V_{\sqrt{2}A_2}^\tau$, J. Pure and Applied Algebra , 218(2014), no. 1, 148-173 59 (with T. Arakawa, H. Yamada) Zhu's algebras, $C_2$-algebras and $C_2$-cofiniteness of parafermion vertex operator algebras, Adv. Math. , 264(2014), 261-295 60 (with H. Shimakura) Classification of holomorphic framed vertex operator algebras of central charge 24, Amer. J. Math , 137(2015), no. 1, 111-137 61 A level-rank duality for parafermion vertex operator algebras of type A, Proc. Amer. Math. Soc. , 142(2014), no. 12, 4133-4142 62 (with C.S. Su) Griess algebras generated by the Griess algebras of two 3A-algebras with a common axis, J. Math Soc. Japan , 67(2015-04), no. 2, 453-476 63 (with H.Y. Chen) An explicit Majorana representation of the group $3^2{:}2$ of $3C$-pure type, Pacific Journal of Mathematics , 271(2014), no. 1, 25-51 64 (with Hsian Yang Chen) Weyl groups and vertex operator algebras generated by Ising vectors satisfying $(2B,3C)$ condition, Rev. Math. Phys. , 26(2014), no. 6, 1450011-(24 pages) 65 (with H. Yamauchi) On 3-transposition groups generated by $\sigma$-involutions associated to $c=4/5$ Virasoro vectors, J. Algebra , 416(2014), 84-121 66 (with R.L. Griess Jr.) Groups of Lie Type, Vertex Algebras, and Modular Moonshine, International Mathematics Research Notices (2015), 0-0