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This book was originally published in 2006. Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.
Mathematical physics. --- Finite groups. --- Finite groups --- Modular functions. --- Modular functions --- Vertex operator algebras. --- Vertex operator algebras
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Vertex operator algebras. --- Quantum field theory --- Mathematical physics
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"This text provides the current state of knowledge on, arguably, one of the most attractive and mysterious mathematical objects: the Monster group. Some 20 experts here share their expertise in this exciting field. Ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas"--
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Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.
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Lie algebras --- Vertex operator algebras --- Group theory --- Mathematical physics --- Algebras, Vertex operator --- Operator algebras
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Mathematical physics --- Quantum field theory --- Vertex operator algebras --- Congresses. --- Congresses. --- Congresses.
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Algebraic topology --- Vertex operator algebras. --- 512.54 --- Vertex operator algebras --- #KVIV:BB --- 512.81 --- Algebras, Vertex operator --- Operator algebras --- Groups. Group theory --- Lie groups --- 512.81 Lie groups --- 512.54 Groups. Group theory
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Topological groups. Lie groups --- Vertex operator algebras --- Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- Algebras, Vertex operator --- Operator algebras --- Vertex operator algebras. --- Algèbres d'opérateurs des sommets. --- Modules (algèbre)
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