griess atop broken tree, in yellow gloves

Robert L. Griess, Jr.


Publication List

Reference to publication or posting (14 September, 2014)

pdf, dvi, comments


Dong, Chongying; Griess, Robert L., Jr.; Lattice-integrality of certain group-invariant integral forms in vertex operator algebras, about 11 pages, arXiv:1405.4476 Submitted.

[VACP] Griess, Robert L.; Lam, Ching Hung; Applications of vertex algebra covering procedures to Chevalley groups and modular moonshine, about 29 pages. arXiv:1308.2270 Submitted pdf

The following items have been published (online or in print).

[Gr13.1] MR3019247 Griess, Robert L.; Lam, Ching Hung; Moonshine paths for 3A and 6A nodes of the extended E8-diagram. J. Algebra 379 (2013), 85112.  
[Gr12.4] MR2977002 Griess, Robert L., Jr. Moonshine paths and a VOA existence proof of the Monster. Recent developments in Lie algebras, groups and representation theory, 165172, Proc. Sympos. Pure Math., 86, Amer. Math. Soc., Providence, RI, 2012. 20D08 (17B69)  
[Gr12.3] MR2928458 Dong, Chongying; Griess, Robert L., Jr. Integral forms in vertex operator algebras which are invariant under finite groups. J. Algebra 365 (2012), 184198. 17B69
17 January, 2012,

MR2975262 Griess, Robert L., Jr.; Lam, Ching Hung A new existence proof of the monster by VOA theory. Michigan Math. J. 61 (2012), no. 3, 555–573. 20D08.
8 March, 2011 arXiv:1103.1414v2 [math.QA]

[Gr12.1] Robert L. Griess, Jr. and Ching Hung Lam, Diagonal lattices and rootless $EE_8$-pairs,
Journal of Pure and Applied Algebra 216 (2012), pp. 154-169 (Posted on arxiv 11 January 2011. )
[Gr11.3] Robert L. Griess, Jr. and Ching Hung Lam, A moonshine path for 5A and associated lattices of ranks 8 and 16, Journal of Algebra, vol 331, April 2011, 338-361; arXiv:1006.390 pdf, dvi
[Gr11.2] Robert L. Griess, Jr. and Ching Hung Lam, Dihedral groups and $EE_8$ lattices, Pure and Applied Math Quarterly (special issue for Jacques Tits) Volume 7, Number 3, 2011, page 621-743.(preprint 87 pages, available at {$\sim$rlg/griesspublicationlist.html}) pdf

Robert L. Griess, Jr. and Ching Hung Lam, A moonshine path from $E_8$ to the monster; Journal of Pure and Applied Algebra, 215 (2011) pp. 927-948. arxiv 11 oct 09).

[Gr10.4] Robert L. Griess, Jr., Nonassociativity in VOA theory and finite group theory, Comment. Math. Univ. Carolin. 51, 2 (2010) 237-244. Preprint at pdf


Robert L. Griess, Jr., Rank 72 high minimum norm lattices, Journal of Number Theory, Volume 130, Issue 7, July 2010, Pages 1512-1519; arxiv 11 oct 09.


[Gr10.2] Robert L. Griess, Jr., "An introduction to groups and lattices: finite groups and positive definite rational lattices"; published 2010 by Higher Education Press (in China) and published in 2011 by the International Press for the rest of the world. No pdf or dvi, sorry. (text is in English)

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Go to Int. Press site

[Gr10.1] Midwest cousins of Barnes-Wall lattices, Journal of Number Theory 130 (2010), pp. 680-695; arxiv 7 jan 09. pdf
[Gr09.2] Special issue of Michigan Math J. 58, Issue 1; dedicated to Donald G. Higman; special issue editors were Eiichi Bannai, Robert Griess, Cheryl Praeger and Len Scott.  
[Gr09.1] The mathematics of Donald Gordon Higman, by Eiichi Bannai, Robert Griess, Cheryl Praeger and Len Scott, Michigan Math J. 58(2009) 3-30. (biography) pdf
[Gr08.2] Few-cosine spherical codes and Barnes-Wall lattices, Journal of Combinatorial Theory, Series A 115 (2008), pp. 1211-1234 pdf
[Gr08.1] Rootless pairs of $EE_8$ lattices, with Ching Hung Lam, Electronic Research Announcements in Mathematical Sciences, 15 (2008) 52-61 pdf
[Gr07.3] Uniqueness results for the moonshine vertex operator algebra, with Chongying Dong and Ching Hung Lam, American Journal of Mathematics, vol. 129, no. 2 (April, 2007), 583 - 609. pdf, com
[Gr07.2] Corrections and additions to `` Pieces of $2^d$: existence and uniqueness for Barnes-Wall and Ypsilanti lattices. '' [Adv. Math. 196 (2005) 147-192], Advances in Mathematics 211 (2007) 819-824. See item [Gr05.1]. pdf
[Gr07.1] Review of the Mark Ronan book ``Symmetry and the Monster, one of the Greatest Quests of Mathematics", Notices AMS, February, 2007, p.234-239. pdf
[Gr05.3] Involutions on the the Barnes-Wall lattices and their fixed point sublattices, I. Pure and Applied Mathematics Quarterly, vol.1, no. 4, (Special Issue: In Memory of Armand Borel, Part 3 of 3) 989-1022, 2005. pdf
[Gr05.2] The rank two lattice type vertex operator algebras $V_L^+$ and their automorphism groups, with Chongying Dong, Michigan Math. J. 53 (2005), no. 3, 691--715. math.QA/0409409

pdf, dvi, com

[Gr05.1] Pieces of $2^d$: existence and uniqueness for Barnes-Wall and Ypsilanti lattices. Advances in Mathematics, 196 (2005) 147-192. math.GR/0403480; for corrections, see [Gr07.2]. pdf, dvi
[Gr03.3] GNAVOA, I. (studies in groups, nonassociative algebras and vertex operator algbras), (about 25 pages) article in Vertex Operator Algebras in Mathematics and Physics, with S. Berman, Y. Billig and J. Lepowsky, Fields Institute Communications, Vol. 39, Amer. Math. Soc., Providence, 2003. pdf, dvi
[Gr03.2] Robert L. Griess, Jr., Positive definite lattices of rank at most 8, Journal of Number Theory, 103 (2003), 77-84. pdf, dvi, com
[Gr03.1] Chongying Dong, Robert L. Griess, Jr. and Gerald H\"ohn, Frame stabilizers for the lattice vertex operator algebra of type $E_8$, J. reine angew. Math., 561 (2003), 1-37. dvi
[Gr02.3] Chongying Dong and Robert L. Griess, Jr. Automorphism groups of finitely generated vertex operator algebras, Michigan Math Journal, 50 (2002). 227-239. math.QA/0106051 dvi
[Gr02.2] Embeddings of $SL(2,27)$ in algebraic groups of type $E_8$, with Alex Ryba, Michigan Math Journal, 50 (2002), 89-99.  
[Gr02.1] Quasisimple finite subgroups of exceptional algebraic groups, with Alex Ryba, Journal of Group Theory, 2002, 1-39. dvi
[Gr01.1] Embeddings of $PSL(2,41)$ and $PSL(2,49)$ in $E_8(C)$ (with A. Ryba) Computational algebra and number theory (Milwaukee, WI, 1996). J. Symbolic Comput. 31 (2001), no. 1-2, 211--227.  
[Gr00.1] Embeddings of $Sz(8)$ into exceptional Lie groups (with A. Ryba), J. reine angew. Math., 523 (2000), 55-68.  
[Gr99.4] Robert L. Griess, Jr., Pieces of Eight, Advances in Mathematics, 148, 75-104 (1999). dvi
[Gr99.3] Automorphisms of vertex operator algebras, a survey, Proceedings of the Raleigh Conference on affine algebras, quantum affine algebras and related topics, 21-24 May, 1998. Contemporary Mathematics, volume 248, American Mathematical Society, 1999.  
[Gr99.2] Rank one lattice type vertex operator algebras and their automorphism groups, II: E-series (with Chongying Dong and A. Ryba), Journal of Algebra 217, 1999, 701-710.  
[Gr99.1] Finite simple groups which projectively embed in an exceptional Lie group are classified! (with A. Ryba), Bulletin Amer. Math. Soc. 36 (1), 1999, 75-93.  
[Gr98.6] A vertex operator algebra related to $E_8$ with automorphism group $O^+(10,2)$, article in The Monster and Lie Algebras, ed. J. Ferrar and K.Harada, deGruyter, Berlin, 1998. pdf
[Gr98.5] Rank one lattice type vertex operator algebras and their automorphism groups (with Chongying Dong), Journal of Algebra 208, 1998, 262-275. q-alg/9710017  
[Gr98.4] Embeddings of $PSL(2,32)$ and $PGL(2, 31)$ in $E_8(C)$ (with A. Ryba), Duke Math. Journal, 94 (1), 1998, 181-211.  
[Gr98.3] The Conjugacy classes of elements in the Borovik group (with D. Frey), Journal of Algebra 203, 1998, 226-243.  
[Gr98.2] Framed vertex operator algebras, codes and the moonshine module, (with Chongying Dong and Gerald H\" ohn), Comm. Math. Physics, 193, 1998, 407-448. pdf comments  
[Gr98.1] Twelve Sporadic Groups, Springer Monographs in Mathematics, 1998, Springer-Verlag. no pdf or dvi, sorry. Please buy my book.
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[Gr95.3] An infinite family of elementwise conjugate nonconjugate homomorphisms, (with P. Fong), International Research Notes in Mathematics No. 5, 1995, 249-252. (J. Arthur, ed.)  
[Gr95.2] Codes, Loops and $p$-Locals, Groups, Difference Sets and the Monster, ed. Joe Ferrar and Koichiro Harada, 1995, 369-375.  
[Gr95.1] Basic Conjugacy Theorems for $G_2$, Inventiones Math. 121, 1995, 257-277.  
[Gr94.2} Minimal dimensions for modular representations of the Monster (with Steve Smith), Comm. Algebra, 22(15), 1994, 6279-6294.  
[Gr94.1] Embeddings of $U_3(8)$, $Sz(8)$ and the Rudvalis group in algebraic groups of type $E_7$ , (with A. Ryba), Inventiones Mathematicae 116, 1994, 1215-241 (special issue dedicated to Armand Borel).  
[Gr93.2] The group $L(2,61)$ embeds in the Lie group of type $E_8$, (with A.Cohen and B. Lisser), Comm. Algebra, 21(6), 1993, 1889-1907.  
[Gr93.1] Non-local Lie primitive subgroups of Lie groups, (with A. Cohen), Canadian Journal of Mathematics, 45, No. 1, 1993, 88-103.  
[Gr92.1] Daniel Frohardt and Robert L. Griess, Jr., Automorphisms of Modular Lie Algebras, Nova Journal of Algebra and Geometry, Vol. 1, No. 4, 1992, 339-345. pdf
[Gr91.1] Elementary Abelian $p$-subgroups of algebraic groups, Geom. Dedicata 39, 1991, 253-305.  
[Gr90.1] A Moufang loop, the exceptional Jordan algebra and a cubic form in 27 variables, J. Algebra, Vol. 131,1990, No. 1, 281-293.  
[Gr89.1] A uniqueness proof for the monster (with U. Meierfrankenfeld and Y. Segev), Annals, 130,1989, 567-602.  
[Gr88.2] Code loops and a large finite group containing triality for $D_4$, Proc. Atti Del Convegno Internazionale di Teoria Dei Gruppi E Geometria Combinatoria, Firenze, 23-25 October 1986, Serie II, 19, 1988, pg.79-98.  
[Gr88.1] On finite simple subgroups of the complex Lie group of type $E_8$ (with A.M. Cohen), Proc. Symp. Pure Math., 47, 1987, 367-405.  
[Gr87.2] The Schur multiplier of McLaughlin's simple group, Arch. Math. Vol. 48, 1987, 31.  
[Gr87.1] Sporadic groups, code loops and nonvanishing cohomology, J. Pure Appl. Algebra, 44, 1987, 191-214.  
[Gr86.2] A structure constant problem of Goddard and Olive, dedicated to Professor Bertram Huppert on the occasion of his sixtieth birthday, in Proceedings of the Montreal Conference on Infinite Dimensional Lie Algebras and their Applications, World Scientific (ed. S. Kass) , 1986  
[Gr86.1] Code loops, J. Algebra, 100, 1986, 224-234.  
[Gr85.3] The monster and its nonassociative algebra, in Proceedings of the Montreal Conference on Finite Groups, Contemporary Mathematics, 45, 121-157, 1985, American Mathematical Society, Providence, RI.  
[Gr85.2] A remark about representations of $\cdot 1$, Comm. Algebra, 13, 1985, 835-844.  
[Gr85.1] A brief introduction to the finite simple groups, in Vertex Operators in Mathematics and Physics, Mathematical Sciences Research Publications 3, (J. Lepowsky, S. Mandelstam, I. Singer, eds.), Springer-Verlag, New York,1985, 217-230.  
[Gr84.2] The sporadic simple groups and construction of the monster, in Proceedings of the International Conference of Math., Warsaw, Polish Scientific Publishers, Warszawa; North Holland, Amsterdam, 1984, 369-384.  
[Gr84.1] Schur multipliers of the known finite simple groups, III, in Proceedings of the Rutgers Groups Theory Year, 1983-1984, 1984, Cambridge University Press, 69-80.  
[Gr83.2] Quotients of infinite reflection groups, Math. Ann., 263, 1983, 267-278.  
[Gr83.1] Finite groups with standard components of Lie type over fields of characteristic two (with R. H. Gilman), J. Algebra, 80, 1983, 383-516.  
[Gr82.2] The friendly giant, Invent. Math., 69, 1982, 1-102.  
[Gr82.1] A construction of $F_1$ as automorphisms of a 196,883-dimensional algebra, Proc. Natl. Acad. Sci., USA, 78, 1981, 689-691.  
[Gr80.2] Schur multipliers of the known finite simple groups, II, The Santa Cruz Conference on Finite Groups, Amer. Math. Soc., Providence, 1980, 279-282.  
[Gr80.1] Odd standard form problems, Proceedings of the Durham Conference (survey article), Academic Press, 1980, 199-206.  
[Gr79.1] Finite groups with unbalancing 2-components of $\{L_3(4),He\}$-type (with
R. Solomon), J. Algebra, 60, 1979, 95-125.
[Gr78.4] Finite groups whose involutions lie in the center, Quarterly J. Math., 29, 1978, 241-247.  
[Gr78.3] A remark about groups of characteristic 2-type and $p$-type, Pacific J. Math., 74, 1978, 349-355.  
[Gr78.2] Bender groups as standard subgroups (with D. R. Mason and G. M. Seitz), Trans. Amer. Math. Soc., 1978, 238, 179-211.  
[Gr78.1] The Frattini module (with P. Schmid), Archiv der Mathematik, 30, 1978, 256-266.  
[Gr77.1] Maximal subgroups and field automorphisms of finite Chevalley groups (with N. Burgoyne and R. Lyons), Pacific J. Math., 71, 1977, 365-403.  
[Gr76.4] Maximal subgroups and field automorphisms of finite Chevalley groups (research announcement for Maximal subgroups and field automorphisms of finite Chevalley groups), Proceedings of the onference on Finite Groups, Park City, Utah, February 1975, Academic Press, Inc.,1976, 329-330.  
[Gr76.3] The splitting of extensions of $SL(3,3)$ by the vector space $\hbox{ \bf F}_3^3$, Pacific J. Math., 63,1976, 405-409.  
[Gr76.2] On a subgroup of order $2^{15}|GL(5,2)|$ in $E_8 (C)$ , the Dempwolff group and $Aut(D_8 \circ D_8 \circ D_8)$ , J. Algebra, 40, 1976, 271-279.  
[Gr76.1] The structure of the `` Monster" simple group, Proceedings of the Conference on Finite Groups, Park City, Utah, February 1975, Academic Press, Inc.,1976, 113-118.  
[Gr75.1] The automorphism group of the Tits simple group ${}^2F_4 (2)'$ (with R. Lyons), Proc. Amer. Math. Soc., 52, 75-78, 1975.  
[Gr74.1] Schur multipliers of some sporadic simple groups, J. Algebra, 32, 445-466, 1974.  
[Gr73.4] Automorphisms of extra special groups and nonvanishing degree 2 cohomology (research announcement for [5]), in Finite Groups 1972: Proceedings of the Gainesville Conference on Finite Groups, (T. Gagen, M. P. Hale and E. E. Shult, eds.), North Holland Publishing Co., Amsterdam, 68-73, 1973.  
[Gr73.3] Automorphisms of extra special groups and nonvanishing degree 2 cohomology, Pacific J. Math., 48, 403-422, 1973.  
[Gr73.2] A characterization of $U_3(2^n)$ by its Sylow 2-subgroup, Trans. Amer. Math. Soc., 175, 181-186, 1973.  
[Gr73.1] Schur multipliers of finite simple groups of Lie type, Trans. Amer. Math. Soc., 183, 355-421, 1973.  
[Gr72.1] Schur multipliers of the known finite simple groups, Bull. Amer. Math. Soc., 78, 68-71, 1972.  
[Gr71.1] Schur Multipliers of the Known Finite Simple Groups, Ph.D. Thesis, University of Chicago, 1971.  
  item in Notices AMS about central extensions  
please inform me if you find any broken links
more to go, under construction, needs editing; pdf or dvi not always available
Vertex operator algebras (VOAs)
Monster and Monster-related
Finite subgroups of Lie groups
Sporadic groups
Finite simple groups
Group cohomology, group extensions
Discrete math