ADE

The ADE diagrams are ubiquitous in mathematics. This book details their occurrences in many areas and develops the theory.

The ADE diagrams arise throughout mathematics, in algebra, geometry, mathematical physics and combinatorics. This book explains these multiple occurrences and develops the theory to understand them. Accessible to students, with exercises and examples throughout, this is an excellent introduction to this unifying principle 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, 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.