ADE: Patterns in Mathematics

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ID: 288065
2025
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Abstract
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.
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Authors John McKay
Journal ADVANCES IN ARCHAEOLOGICAL PRACTICE
Year 2025
DOI
10.1017/9781009335935
URL
https://www.cambridge.org/core/books/ade/6478B3D4CEEF045E0E6F2828AD4E4AD7
Keywords Keywords not found

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