ADE, 9781009335980
Paperback
Ancient shapes unlock hidden secrets linking groups, algebras, and beyond.
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$76.18

  • Paperback

    198 pages

  • Release Date

    31 July 2025

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Summary

The ADE Mystery: Unveiling Connections Across Mathematics

John McKay’s groundbreaking work reveals a profound link between the ‘double covers’ of regular polyhedral groups, familiar since ancient Greece, and the exceptional Lie algebras, identified in the late nineteenth century. This connection centers on the ADE diagrams, versatile structures with multiple interpretations.

These diagrams serve as:

  • Quivers associated with the polyhedral groups.
  • Dynkin…

Book Details

ISBN-13:9781009335980
ISBN-10:1009335987
Series:London Mathematical Society Student Texts
Author:Peter J. Cameron, Pierre-Philippe Dechant, Yang-Hui He, John McKay
Publisher:Cambridge University Press
Imprint:Cambridge University Press
Format:Paperback
Number of Pages:198
Release Date:31 July 2025
Weight:0g
About The Author

Peter J. Cameron

Peter J. Cameron is currently a part-time professor at the University of St Andrews. He was chair of the British Combinatorial Committee for nearly thirty years and won the Junior and Senior Whitehead Prizes of the LMS. Cameron has been fascinated by ADE since using it to prove a conjecture of Alan Hoffman.

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.

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