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Academic Staff

Lam, Ching Hung

Lam, Ching Hung

Research Fellow

Research Fields: Algebra,

Email : chlam@math.sinica.edu.tw

Extension : 705

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.

  • Ph.D. Ohio State University 1996
  • B.A. (2nd class honour, division 1) University of Hong Kong 1989
  • B.A. University of Hong Kong

  • Deputy Director Institute of Mathematics, Academia Sinica 2013/8 - 2019/11
  • Research Fellow Academia Sinica, Taiwan 2009 - Present
  • Professor National Cheng Kung University 2004 - 2009
  • Associate Professor National Cheng Kung University 2001 - 2004
  • Assistant Professor National Cheng Kung University 2000 - 2001
  • Research Associate University of Tsukuba 1997 - 2000
  • Lecturer Ohio State University 1996 - 1997

  • 2009-2011, Outstanding Research Award, National Science Council, Taiwan, R.O.C.
  • 2008, Distinguished Professor, National Cheng Kung University

  • (with Cuipo Jiang, Hiroshi Yamauchi) "The classification of vertex operator algebras of OZ-type generated by Ising vectors of $\sigma$-type", 2024, Link
  • (with Hsian-Yang Chen) "Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras", 2024, Link
  • (with Hiroki Shimakura) "Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras", Journal of Pure and Applied Algebra , 228, 2024, Link
  • (with Drazen Adamovic, Veronika Pedic Tomic, Nina Yu) "On irreducibility of modules of Whittaker type: twisted modules and nonabelian orbifolds", 2023, Link
  • (with Masahiko Miyamoto) "A lattice theoretical interpretation of generalized deep holes of the Leech lattice vertex operator algebra", Forum of Mathematics, Sigma, 11 (e86), 2023, Link
  • "Unitary forms for holomorphic vertex operator algebras of central charge 24", Letters in Mathematical Physics, 113 (2), 2023, Link, Link
  • (with Koichi Betsumiya, Hiroki Shimakura) "Automorphism Groups and Uniqueness of Holomorphic Vertex Operator Algebras of Central Charge 24", Communications in Mathematical Physics , 399 (3), 1773-1810, 2023, Link, Link
  • (with Naoki Chigira, Masahiko Miyamoto) "Orbifold construction and Lorentzian construction of Leech lattice vertex operator algebra", J. Algebra, 593, 26-71, 2022-03 , Link
  • (with Hiroshi Yamauchi) "The Conway-Miyamoto correspondences for the Fischer 3-transposition groups", Transactions of American Mathematical Society , 375 (3), 2025-2067, 2022-03 , Link
  • (with Koichi Betsumiya, Hiroki Shimakura) "Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries", Israel Journal of Mathematics, 2022
  • (with Hiromichi Yamada) "Sigma involutions associated with parafermion vertex operator algebra $K(sl_2,k)$", Linear and Multilinear Algebra, 70 (21), 6780-6819, 2022, Link
  • (with Hsian-Yang Chen) "Fourvolutions and automorphism groups of orbifold lattice vertex operator algebras", Taiwanese J. Math. , 25 (6), 1173-1185, 2021-12 , Link, Link
  • (with Jethro van Ekeren, Sven Möller, Hiroki Shimakura) "Schellekens' list and the very strange formula", Advances in Mathematics, 380, 2021-03 , Link
  • (with J. Connor Grady, James E. Tener, Hiroshi Yamauchi) "Classification of extremal vertex operator algebras with two simple modules", Journal of Mathematical Physics, 61 (5), 2020, Link
  • (with Lin, Xingjun) "A holomorphic vertex operator algebra of central charge 24 with the weight one Lie algebra $F_{4,6}A_{2,2}$", J. Pure Appl. Algebra, 224 (3), 1241-1279, 2020, Link
  • "Cyclic orbifolds of lattice vertex operator algebras having group-like fusions", Letters in Mathematical Physics, 110 (5), 1081-1112, 2020, Link, Link
  • (with Hiroki Shimakura) "Inertia groups and uniqueness of holomorphic vertex operator algebras", Transformation groups, 25 (4), 1223-1268, 2020, Link, Link
  • (with H. Shimakura) "On orbifold constructions associated with the Leech lattice vertex operator algebra", Mathematical Proceedings of the Cambridge Philosophical Society. , 168 (2), 261-285, 2020, Link
  • (with Hiroki Shimakura) "Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras", Trans. Amer. Math. Soc., 372 (10), 7001-7024, 2019-11 , Link
  • (with T. Arakawa, H. Yamada) "Parafermion vertex operator algebras and W-algebras", Trans. Amer. Math. Soc., 371 (6), 4277-4301, 2019-03 , Link
  • (with D. Adamovic, V. Pedić, N. Yu ) "On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebras", J. Algebra, 539, 1-23, 2019
  • (with C. P. Jiang, H. Yamauchi) "Vertex operator algebras generated by Ising vectors of $\sigma$-type", Mathematische Zeitschrift , 293 (1月2日), 425-442, 2019, Link
  • (with C. P. Jiang) "Level-Rank Duality for Vertex Operator Algebras of types B and D", Bull. Inst. Math. Acad. Sin. (N.S.), 14 (1), 31-54, 2019, Link, Link
  • (with Hiroshi Yamauchi) "3-dimensional Griess algebras and Miyamoto involutions", Bull. Inst. Math. Acad. Sin. (N.S.), 14 (2), 119-147, 2019, Link, Link
  • (with T. Abe, H. Yamada) "On $\mathbb{Z}_p$-orbifold constructions of the Moonshine vertex operator algebra", Mathematische Zeitschrift, 290 (1), 683-, 2018-10 , Link, Link
  • (with T. Abe, H. Yamada) "Extensions of tensor products of $\mathbb{Z}_p$-orbifold models of the lattice vertex operator algebra $V_{\sqrt{2}A_{p-1}}$", J. Algebra , 510, 24-, 2018, Link
  • (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, 288 (1月2日), 75-, 2018, Link, Link
  • (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", Proceedings of Amer. Math. Soc. , 146 (5), 1937-1950, 2018, Link
  • (with H.Y. Chen ) "Quantum dimensions and fusion rules of the VOA $V_{L_{C\times D}}^\tau$", Journal of Algebra, 459, 309-349, 2016-08 , Link
  • (with H. Shimakura) "Orbifold construction of holomorphic vertex operator algebras associated to inner automorphisms", Communications in Mathematical Physics, 342 (3), 803-841, 2016-03 , Link
  • (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, 1575-1585, 2016, Link, Link
  • (with C.S. Su) "Griess algebras generated by the Griess algebras of two 3A-algebras with a common axis", J. Math Soc. Japan, 67 (2), 453-476, 2015-04
  • (with R.L. Griess Jr.) "Groups of Lie Type, Vertex Algebras, and Modular Moonshine", International Mathematics Research Notices, 2015, Link
  • (with H. Shimakura) "Classification of holomorphic framed vertex operator algebras of central charge 24", Amer. J. Math, 137 (1), 111-137, 2015
  • (with H. Yamauchi) "On 3-transposition groups generated by $\sigma$-involutions associated to $c=4/5$ Virasoro vectors", J. Algebra, 416, 84-121, 2014
  • (with H.Y. Chen) "An explicit Majorana representation of the group $3^2{:}2$ of $3C$-pure type ", Pacific Journal of Mathematics , 271 (1), 25-51, 2014
  • (with Hsian Yang Chen) "Weyl groups and vertex operator algebras generated by Ising vectors satisfying $(2B,3C)$ condition", Rev. Math. Phys. , 26 (6), 2014
  • "A level-rank duality for parafermion vertex operator algebras of type A", Proc. Amer. Math. Soc., 142 (12), 4133-4142, 2014
  • (with T. Arakawa, H. Yamada) " Zhu's algebras, $C_2$-algebras and $C_2$-cofiniteness of parafermion vertex operator algebras", Adv. Math. , 264, 261-295, 2014
  • (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 (1), 148-173, 2014
  • (with C.S. Su) "Griess algebras generated by 3 Ising vectors of central 2A-type", J. algebra, 374, 141-166, 2013
  • (with R.L. Griess) "Moonshine paths for $3A$ and $6A$ nodes of the extended $E_8$-diagram", J. Algebra, 379, 85-112, 2013
  • (with Masaaki Harada; Akihiro Munemasa) "Residue codes of extremal Type II $\mathbb{Z}_4$-codes and the moonshine vertex operator algebra", Math. Z. , 274 (1), 685-700, 2013
  • (with Robert L.~Griess Jr.) "A new existence proof of the Monster by VOA theory", Michigan Mathematical Journal, 61, 555-573, 2012, Link
  • (with R.L. Griess, Jr. ) "Diagonal lattices and rootless $EE_8$ pairs", J. Pure and Applied Algebra, 216 (1), 154-169, 2012
  • (with H. Shimakura) "Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24", Proceedings of the London Mathematical Society, 104 (3), 540-576, 2012
  • (with G. Hoehn, H. Yamauchi) "McKay's $E_6$ observation on the largest Fischer group", Comm. Math. Phys. , 310, 329-365, 2012
  • (with Gerald Hoehn; Hiroshi Yamauchi) "McKay's $E_7$ observations on the Baby Monster ", Inter. Math. Res. Not. , 2012, 166-212, 2012
  • "On the constructions of holomorphic vertex operator algebras of central charge 24", Comm. Math. Phys., 305 (1), 153-198, 2011
  • (with Robert L. Griess Jr.) "A moonshine path for $5A$ and associated lattices of ranks 8 and 16", J. Algebra, 331, 338-361, 2011
  • (with R. L. Griess ) "A moonshine path from $E_8$ to the Monster", J. Pure and Applied Algebra, 215, 927-948, 2011
  • (with R.L. Griess Jr.) "Dihedral groups and Sums of $EE_8$-lattices", Pure and applied mathematics quarterly, 7 (3), 621-743, 2011
  • (with C. Dong, Q. Wang and H. Yamada) "The structure of parafermion vertex operator algebras", J. Algebra, 323 (2), 371-381, 2010
  • (with C. Dong,and H. Yamada) "W-algebras related to parafermion algebras", J. Algebra, 332, 2236-2043, 2009
  • (with H. Shimakura) "Frame Stabilizers for Framed Vertex Operator Algebras Associated to Lattices Having 4-Frames", Int. Math. Res. Notices, 2009, 4547-4577, 2009
  • (with S. Sakuma) "On a class of vertex operator algebras having a faithful $S_{n+1}$-action", Taiwanese J. Math, 12 (9), 2465-2488, 2008, Link
  • (with R.L. Griess Jr.) "Rootless pairs of EE8-lattices", Electronic Research Announcements in Mathematical Sciences, 15, 52-61, 2008
  • (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 (35), 25-35, 2008
  • (with H. Yamauchi) "On the structure of framed vertex operator algebras and their pointwise frame stabilizers", Commun. Math. Phys., 277 (1), 237-285, 2008
  • (with H. Shimakura) "Ising vectors in the vertex operator algebra $V_{\Lambda}^+$ associated with the Leech lattice Λ", Intern. Math. Res., 2007, 2007
  • (with H. Yamauchi) "A characterization of the moonshine vertex operator algebra by means of Virasoro frames", Intern. Math. Res. Notices, 2007, 2007
  • (with T. S. Chen) "Extension of the tensor product of unitary Virasoro vertex operator algebras", Communications in Algebras, 35 (8), 2487-2505, 2007
  • (with C. Dong, R. L. Griess) "Uniqueness results of Frenkel–Lepowsky -Meurman's moonshine vertex operator algebra", American Journal of Mathematics, 129 (2), 583-609, 2007
  • (with S. Sakuma and H. Yamauchi) "Ising vectors and automorphism groups of commutant subalgebras related to root systems", Mathematische Zeitschrift, 255 (3), 597-626, 2007
  • (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 (9), 4107-4123, 2007
  • (with M. Miyamoto) "Niemeier Lattices, Coxeter elements and McKay's E8 observation on the Monster simple group", Intern. Math. Res. Notices, 2006
  • (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, 117-181, 2005
  • (with Yamada H) "Tricritical 3-state Potts model and vertex operator algebras constructed from ternary codes", Communications in Algebra, 32 (11), 4197-4219, 2004
  • (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 (5), 245-296, 2004
  • (with H. Yamada) "Decomposition of the lattice vertex operator algebra $V_{\sqrt{2}A_{\ell}}$", Journal of Algebra, 272 (2), 614-624, 2004
  • (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, 1269-1303, 2003
  • (with N. Lam, and H. Yamauchi) "Extension of unitary Virasoro vertex operator algebra by a simple module", International Mathematics Research Notices, 11, 577-611, 2003
  • (with H. Yamada) "$\mathbb{Z}_3$-twisted representations of lattice vertex operator algebras", Communications in Algebra, 31 (6), 3001-3020, 2003
  • (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 (1), 15-48, 2002
  • (with M. Kitazume, and H. Yamada) "A class of vertex operator algebras constructed from $\mathbb{Z}_8$-codes", Journal of Algebra, 338-359, 2001
  • "Induced modules for orbifold vertex operator algebras", Journal of Mathematical Society of Japan, 53 (3), 541-557, 2001, Link
  • "Fusion rules for Hamming code vertex operator algebra", Communications in Algebra, 29 (5), 2125-2145, 2001
  • (with C. Dong,and H. Yamada) "Decomposition of the vertex operator algebra $V_{\sqrt{2}D_n}$", Communications in Contemporary Mathematics, 3 (1), 137-151, 2001
  • "Representations of ternary code vertex operator algebras", Communications in Algebra, 29 (3), 951-971, 2001
  • "Some twisted modules for framed vertex operator algebras", Journal of Algebra, 231, 331-341, 2000
  • (with K.Kitazume, and H. Yamada) "Decomposition of the Moonshine vertex operator algebra as Virasoro modules", Journal of Algebra, 226, 893-919, 2000
  • (with H. Yamada) "$\mathbb{Z}_2\times \mathbb{Z}_2$ codes and vertex operator algebras", Journal of Algebra, 224, 268-291, 2000
  • (with C. Dong,and H. Yamada) "Decomposition of the vertex operator algebra $V_{\sqrt{2}A_3}$", Journal of Algebra, 222, 500-510, 1999
  • "Code vertex operator algebras under coordinates change", Communications in Algebra, 27 (9), 4587-4605, 1999
  • "Twisted repesentations of code vertex operator algebras", Journal of Algebra, 217 (7), 275-299, 1999
  • "On VOA associated with special Jordan algebras", Communications in Algebra, 27 (4), 1665-1681, 1999
  • " Construction of vertex operator algebras form commutative associative algebras", Communications in Algebra, 24 (14), 4439-4460, 1996
  • (with K. Harada) "Inverses' of Virasoro operators", Communications in Algebra, 23 (12), 4405-4413, 1995
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