ADE: Patterns in Mathematics - Couverture rigide

Cameron, Peter J.; Dechant, Pierre-Philippe; He, Yang-Hui; McKay, John

Couverture rigide

ISBN 10 : 1009335960 ISBN 13 : 9781009335966

Editeur : Cambridge University Press, 2025

Synopsis

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.

A propos du livre

À propos des auteurs

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.

Détails de l'édition

• Éditeur: Cambridge University Press
• Date d'édition: 2025
• Langue: anglais
• ISBN 10: 1009335960
• ISBN 13: 9781009335966
• Reliure: Relié
• Nombre de pages: 196
• Coordonnées du fabricant: Cambridge University Press; https://www.cambridge.org/; ; Via Honduras,15; Pomezia; Italia; 71; Italie