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Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Book Review

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Book Information

Author(s): Terry Gannon
Title: Moonshine beyond the monster: The bridge connecting algebra, modular forms and physics
Additional book information: Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, Massachusetts, 2006, 492 pp., US$130.00, ISBN 978-0-521-83531-2

References:

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Conway, J. H.; Norton, S. P. Monstrous moonshine. Bull. London Math. Soc. 11 (1979), no. 3, 308-339. MR 554399 (81j:20028)

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Conway, John H.; Norton, Simon P.; Soicher, Leonard H. The Bimonster, the group $ Y_{555}$, and the projective plane of order 3. Computers in algebra (Chicago, IL, 1985), 27-50, Lecture Notes in Pure and Appl. Math., 111, Dekker, New York, 1988. MR 1060755 (92f:20018)

[DLM]
Dong, Chongying; Li, Haisheng; Mason, Geoffrey. Modular-invariance of trace functions in orbifold theory and generalized Moonshine. Comm. Math. Phys. 214 (2000), no. 1, 1-56. MR 1794264 (2001k:17043)

[D]
Duncan, John F. Moonshine for Rudvalis's sporadic group I, arXiv:math/0609449

[FLM]
Frenkel, I. B.; Lepowsky, J.; Meurman, A. A natural representation of the Fischer-Griess Monster with the modular function $ J$ as character. Proc. Nat. Acad. Sci. U.S.A. 81 (1984), no. 10, Phys. Sci., 3256-3260. MR 747596 (85e:20018)

[G]
Griess, Robert L., Jr. The friendly giant. Invent. Math. 69 (1982), no. 1, 1-102. MR 671653 (84m:20024)

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Hirzebruch, Friedrich; Berger, Thomas; Jung, Rainer. Manifolds and modular forms. Aspects of Mathematics, E20. Friedr. Vieweg & Sohn, Braunschweig, 1992. xii+211 pp. ISBN: 3-528-06414-5 MR 1189136 (94d:57001)

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Mahowald, Mark; Hopkins, Mike. The structure of 24 dimensional manifolds having normal bundles which lift to BO[8]. Recent progress in homotopy theory (Baltimore, MD, 2000), 89-110, Contemp. Math., 293, Amer. Math. Soc., Providence, RI, 2002. MR 1887530 (2003b:55007)

[I]
Ivanov, A. A. A geometric characterization of the Monster. Groups, combinatorics & geometry (Durham, 1990), 46-62, London Math. Soc. Lecture Note Ser., 165, Cambridge Univ. Press, Cambridge, 1992. MR 1200249 (94c:20033)

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Kac, V. G. An elucidation of: ``Infinite-dimensional algebras, Dedekind's $ \eta$-function, classical Möbius function and the very strange formula''. $ E_{8^{}}^{(1)}$ and the cube root of the modular invariant $ j$. Adv. in Math. 35 (1980), no. 3, 264-273. MR 563927 (83a:17014b)

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Kawahigashi, Yasuyuki; Longo, Roberto. Local conformal nets arising from framed vertex operator algebras. (English summary) Adv. Math. 206 (2006), no. 2, 729-751. MR 2263720 (2007m:81141)

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Lam, Ching Hung; Miyamoto, Masahiko. Niemeier lattices, Coxeter elements, and McKay's $ E_8$-observation on the Monster simple group. Int. Math. Res. Not. 2006, Art. ID 35967 MR 2219232 (2007b:17041)

[M]
Miyamoto, Masahiko. 21 involutions acting on the Moonshine module. (English summary) J. Algebra 175 (1995), no. 3, 941-965. MR 1341752 (96h:20034)

[Ra]
Ray, U. Automorphic Forms and Lie Superalgebras (Algebra and Applications) Springer; 1 edition (December 2006) ISBN 978-1402050091 MR 2286867

[Ry]
Ryba, A. J. E. Modular Moonshine? Moonshine, the Monster, and related topics (South Hadley, MA, 1994), 307-336, Contemp. Math., 193, Amer. Math. Soc., Providence, RI, 1996. MR 1372729 (97c:20022)

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Smith, Stephen D. On the head characters of the Monster simple group. Finite groups--coming of age (Montreal, Que., 1982), 303-313, Contemp. Math., 45, Amer. Math. Soc., Providence, RI, 1985. MR 822245 (87h:20037)

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Thompson, J. G. Some numerology between the Fischer-Griess Monster and the elliptic modular function. Bull. London Math. Soc. 11 (1979), no. 3, 352-353. MR 554402 (81j:20030)

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Additional Information:

Reviewer(s):
R. E. Borcherds
Affiliation: University of California at Berkeley

Review Information:
Journal: Bull. Amer. Math. Soc. 45 (2008), 675-679.

MSC (2000): Primary 17B69; Secondary 11F22, 20C34, 20D08
DOI: 10.1090/S0273-0979-08-01209-3
PII: S 0273-0979(08)01209-3
Posted: June 25, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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