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Moonshine, the Monster, and Related Topics

Edited by: Chongying Dong University of California, Santa Cruz, Santa Cruz, CA
Geoffrey Mason University of California, Santa Cruz, Santa Cruz, CA
Available Formats:
Electronic ISBN: 978-0-8218-7784-5
Product Code: CONM/193.E
368 pp
List Price: $91.00 MAA Member Price:$81.90
AMS Member Price: $72.80 Click above image for expanded view Moonshine, the Monster, and Related Topics Edited by: Chongying Dong University of California, Santa Cruz, Santa Cruz, CA Geoffrey Mason University of California, Santa Cruz, Santa Cruz, CA Available Formats:  Electronic ISBN: 978-0-8218-7784-5 Product Code: CONM/193.E 368 pp  List Price:$91.00 MAA Member Price: $81.90 AMS Member Price:$72.80
• Book Details

Contemporary Mathematics
Volume: 1931996
MSC: Primary 20; 81; 11; Secondary 80;

“One of the great legacies of the classification of the finite simple groups is the existence of the Monster $\ldots$ Work of Borcherds and Frenkel-Lepowsky-Meurman led to the notion of a vertex (operator) algebra, which was seen to be the same as the chiral algebras used by physicists in conformal field theory$\ldots$ The connections with physics have proven to be invaluable, and it seems likely that another branch of mathematics whose origins are eerily similar to those of moonshine—that is, elliptic cohomology—will turn out to be very relevant too. — from the Preface

This volume contains the proceedings of a Joint Summer Research Conference held at Mount Holyoke College in June 1994. As perhaps the first conference proceedings devoted exclusively to the subject known as “Moonshine”, this work contains something for many mathematicians and physicists.

Features:

• Results concerning the monster simple group and other simple groups.
• Connections with elliptic cohomology.
• Connections with 2-dimensional conformal field theory.
• Connections with modular functions.

Much of Moonshine, the Monster, and Related Topics features new results not available anywhere else.

Research mathematicians and theoretical physicists interested in the connections among finite groups.

• Articles
• P. Bántay - Higher genus Moonshine [ MR 1372714 ]
• L. Dolan - Superstring twisted conformal field theory [ MR 1372715 ]
• Chongying Dong, Haisheng Li and Geoffrey Mason - Some twisted sectors for the Moonshine module [ MR 1372716 ]
• Alex J. Feingold, John F. X. Ries and Michael D. Weiner - Spinor construction of the $c=\frac 12$ minimal model [ MR 1372717 ]
• Koichiro Harada and Mong Lung Lang - The McKay-Thompson series associated with the irreducible characters of the Monster [ MR 1372718 ]
• Tim Hsu - Some quilts for the Mathieu groups [ MR 1372719 ]
• Yi-Zhi Huang - A nonmeromorphic extension of the Moonshine module vertex operator algebra [ MR 1372720 ]
• A. A. Ivanov - On the Buekenhout-Fischer geometry of the Monster [ MR 1372721 ]
• Takashi Kimura - Operads of moduli spaces and algebraic structures in conformal field theory [ MR 1372722 ]
• J. Lepowsky and R. L. Wilson - On Hopf algebras and the elimination theorem for free Lie algebras [ MR 1372723 ]
• Hai-Sheng Li - Local systems of twisted vertex operators, vertex operator superalgebras and twisted modules [ MR 1372724 ]
• Kefeng Liu - Modular forms and topology [ MR 1372725 ]
• Yves Martin - On modular invariance of completely replicable functions [ MR 1372726 ]
• Kailash C. Misra - On embedding of integrable highest weight modules of affine Lie algebras [ MR 1372727 ]
• S. Norton - The Monster algebra: some new formulae [ MR 1372728 ]
• A. J. E. Ryba - Modular Moonshine? [ MR 1372729 ]
• Gene Ward Smith - Replicant powers for higher genera [ MR 1372730 ]
• Michael P. Tuite - Generalised Moonshine and abelian orbifold constructions [ MR 1372731 ]
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Volume: 1931996
MSC: Primary 20; 81; 11; Secondary 80;

“One of the great legacies of the classification of the finite simple groups is the existence of the Monster $\ldots$ Work of Borcherds and Frenkel-Lepowsky-Meurman led to the notion of a vertex (operator) algebra, which was seen to be the same as the chiral algebras used by physicists in conformal field theory$\ldots$ The connections with physics have proven to be invaluable, and it seems likely that another branch of mathematics whose origins are eerily similar to those of moonshine—that is, elliptic cohomology—will turn out to be very relevant too. — from the Preface

This volume contains the proceedings of a Joint Summer Research Conference held at Mount Holyoke College in June 1994. As perhaps the first conference proceedings devoted exclusively to the subject known as “Moonshine”, this work contains something for many mathematicians and physicists.

Features:

• Results concerning the monster simple group and other simple groups.
• Connections with elliptic cohomology.
• Connections with 2-dimensional conformal field theory.
• Connections with modular functions.

Much of Moonshine, the Monster, and Related Topics features new results not available anywhere else.

Research mathematicians and theoretical physicists interested in the connections among finite groups.

• Articles
• P. Bántay - Higher genus Moonshine [ MR 1372714 ]
• L. Dolan - Superstring twisted conformal field theory [ MR 1372715 ]
• Chongying Dong, Haisheng Li and Geoffrey Mason - Some twisted sectors for the Moonshine module [ MR 1372716 ]
• Alex J. Feingold, John F. X. Ries and Michael D. Weiner - Spinor construction of the $c=\frac 12$ minimal model [ MR 1372717 ]
• Koichiro Harada and Mong Lung Lang - The McKay-Thompson series associated with the irreducible characters of the Monster [ MR 1372718 ]
• Tim Hsu - Some quilts for the Mathieu groups [ MR 1372719 ]
• Yi-Zhi Huang - A nonmeromorphic extension of the Moonshine module vertex operator algebra [ MR 1372720 ]
• A. A. Ivanov - On the Buekenhout-Fischer geometry of the Monster [ MR 1372721 ]
• Takashi Kimura - Operads of moduli spaces and algebraic structures in conformal field theory [ MR 1372722 ]
• J. Lepowsky and R. L. Wilson - On Hopf algebras and the elimination theorem for free Lie algebras [ MR 1372723 ]
• Hai-Sheng Li - Local systems of twisted vertex operators, vertex operator superalgebras and twisted modules [ MR 1372724 ]
• Kefeng Liu - Modular forms and topology [ MR 1372725 ]
• Yves Martin - On modular invariance of completely replicable functions [ MR 1372726 ]
• Kailash C. Misra - On embedding of integrable highest weight modules of affine Lie algebras [ MR 1372727 ]
• S. Norton - The Monster algebra: some new formulae [ MR 1372728 ]
• A. J. E. Ryba - Modular Moonshine? [ MR 1372729 ]
• Gene Ward Smith - Replicant powers for higher genera [ MR 1372730 ]
• Michael P. Tuite - Generalised Moonshine and abelian orbifold constructions [ MR 1372731 ]
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