Electronic ISBN:  9780821877845 
Product Code:  CONM/193.E 
368 pp 
List Price:  $91.00 
MAA Member Price:  $81.90 
AMS Member Price:  $72.80 

Book DetailsContemporary MathematicsVolume: 193; 1996MSC: 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 FrenkelLepowskyMeurman 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 2dimensional conformal field theory.
 The role of operads.
 Connections with modular functions.
Much ofMoonshine, the Monster, and Related Topics features new results not available anywhere else.ReadershipResearch mathematicians and theoretical physicists interested in the connections among finite groups.

Table of Contents

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 McKayThompson series associated with the irreducible characters of the Monster [ MR 1372718 ]

Tim Hsu  Some quilts for the Mathieu groups [ MR 1372719 ]

YiZhi Huang  A nonmeromorphic extension of the Moonshine module vertex operator algebra [ MR 1372720 ]

A. A. Ivanov  On the BuekenhoutFischer 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 ]

HaiSheng 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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“One of the great legacies of the classification of the finite simple groups is the existence of the Monster \(\ldots\) Work of Borcherds and FrenkelLepowskyMeurman 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 2dimensional conformal field theory.
 The role of operads.
 Connections with modular functions.
Much of
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 McKayThompson series associated with the irreducible characters of the Monster [ MR 1372718 ]

Tim Hsu  Some quilts for the Mathieu groups [ MR 1372719 ]

YiZhi Huang  A nonmeromorphic extension of the Moonshine module vertex operator algebra [ MR 1372720 ]

A. A. Ivanov  On the BuekenhoutFischer 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 ]

HaiSheng 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 ]