nLab
Freudenthal magic square

Context

Algebra

Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Exceptional structures

Contents

Idea

A special square array of Lie algebras/Lie groups labeled by pairs of normed division algebras and including all the exceptional Lie groups except G2. Three constructions give this square, namely, the Tits construction, the Vinberg construction and the triality construction (see BaezMagic).

Michael Atiyah (AtiyahMagic) has proposed using the magic square to explain the Kervaire invariant problem similarly to how the existence of the four normed division algebras explains the Hopf invariant one problem.

Extensions

References

See also

Discussion in relation to super Yang-Mills theory, supergravity and U-duality includes

See also at supersymmetry and division algebras.