ADE: Patterns in Mathematics (London Mathematical Society Student Texts, Series Number 109)
Author:Peter J. Cameron (Author), Pierre-Philippe Dechant (Author), Yang-Hui He (Author), John McKay (Author)
Publisher finelybook 出版社: Cambridge University Press
Publication Date 出版日期: 2025-08-07
Language 语言: English
Print Length 页数: 198 pages
ISBN-10: 1009335960
ISBN-13: 9781009335966
Book Description
The ADE diagrams, shown on the cover, constitute one of the most universal and mysterious patterns in all of mathematics. John McKay’s remarkable insights unveiled a connection between the ‘double covers’ of the groups of regular polyhedra, known since ancient Greek times, and the exceptional Lie algebras, recognised since the late nineteenth century. The correspondence involves the ADE diagrams being interpreted in different ways: as quivers associated with the groups and as Dynkin diagrams of root systems of Lie algebras. The ADE diagrams arise in many areas of mathematics, including topics in algebraic geometry, string theory, spectral theory of graphs and cluster algebras. Accessible to students, this book explains these connections with exercises and examples throughout. An excellent introduction for students and researchers wishing to learn more about this unifying principle of mathematics, it also presents standard undergraduate material from a novel perspective.
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Book Description
About the Author
Pierre-Philippe Dechant is a Curriculum Redefined Lecturer in Mathematics and Data Science at the University of Leeds. He is a Senior Fellow of the Higher Education Academy, a Fellow of the Institute of Physics and a Fellow of the Institute for Mathematics and its Applications.
Yang-Hui He is a Fellow at the London Institute and tutor in mathematics at Merton College, Oxford. He also holds honorary professorships at the Universities of London and Nankai. Yang works on geometry, number theory and string theory, and is a pioneer of AI-assisted mathematics.
John McKay was a British-Canadian Mathematician and Professor Emeritus in the Department of Mathematics and Statistics at Concordia University before his death in 2022. He was elected a Fellow of the Royal Society of Canada in 2000, and in 2003 won the CRM-Fields Prize for Mathematics. His groundbreaking contributions include Moonshine, the ADE correspondence and the McKay conjecture on group representations.
