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Product details:
- Publisher Cambridge University Press
- Date of Publication 7 August 2025
- ISBN 9781009335980
- Binding Paperback
- No. of pages196 pages
- Size 228x151x11 mm
- Weight 300 g
- Language English 676
Categories
Short description:
The ADE diagrams are ubiquitous in mathematics. This book details their occurrences in many areas and develops the theory.
MoreLong 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.
MoreTable of Contents:
Nomenclature; 1. An invitation; 2. Algebraic preliminaries; 3. ADE classifications; 4. ADE correspondences; 5. Advanced miscellany; References; Index.
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