ADE : Patterns in Mathematics (London Mathematical Society Student Texts)

Cameron, Peter J./ Dechant, Pierre-Philippe/ He, Yang-Hui

Cambridge University Press（2025/07発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 198 p.
• 言語 ENG
• 商品コード 9781009335980

Full Description

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, recognized since the late nineteenth century. The correspondence involves certain diagrams, the ADE diagrams, which can be interpreted in different ways: as quivers associated with the groups, and Dynkin diagrams of root systems of Lie algebras. The ADE diagrams arise in many areas of mathematics, including topics in relativity and 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.

Contents

Nomenclature; 1. An invitation; 2. Algebraic preliminaries; 3. ADE classifications; 4. ADE correspondences; 5. Advanced miscellany; References; Index.