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  • Publisher:
    Cambridge University Press
    Publication date:
    August 2025
    August 2025
    ISBN:
    9781009335935
    9781009335966
    9781009335980
    DOI:
    https://doi.org/10.1017/9781009335935
    Dimensions:
    (229 x 152 mm)
    Weight & Pages:
    0.435kg, 196 Pages
    Dimensions:
    (229 x 152 mm)
    Weight & Pages:
    0.3kg, 196 Pages
    • Subjects:
    Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
    Series:
    London Mathematical Society Student Texts (109)
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    Subjects:
    Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
    Series:
    London Mathematical Society Student Texts (109)
    Information

    Book 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.

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