Moonshine beyond the Monster : The Bridge Connecting Algebra, Modular Forms and Physics (Cambridge Monographs on Mathematical Physics)

Gannon, Terry

Cambridge University Press（2006/09発売）

• 製本 Hardcover:ハードカバー版／ページ数 492 p.
• 言語 ENG
• 商品コード 9780521835312
• DDC分類 510

基本説明

New in paperback. Hardcover was published in 2006. 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.

Full Description

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.

Contents

Acknowledgements; Introduction: glimpses of the theory beneath Monstrous moonshine; 1. Classical algebra; 2. Modular stuff; 3. Gold and brass: affine algebras and generalisations; 4. Conformal field theory: The physics of Moonshine; 5. Vertex operator algebras; 6. Modular group representations throughout the realm; 7. Monstrous Moonshine; Epilogue; Notation; References; Index.