nLab exceptional structures -- contents

exceptional structures, exceptional isomorphisms

Examples

• exceptional finite groups

  • monster group

  • Mathieu group,

  • Conway group

• exceptional finite rotation groups:

  • tetrahedral group

  • octahedral group

  • icosahedral group

• exceptional Lie groups

  • G₂

  • F₄

  • E₆, E₇, E₈

  and Kac-Moody groups:

  • E₉, E₁₀, E₁₁, …

• Dwyer-Wilkerson H-space

• exceptional Lie algebras

• exceptional Jordan algebra

  • Albert algebra

• exceptional Jordan superalgebra, $K_10$

• E₈ lattice, Leech lattice

• Cayley plane

Interrelations

• supersymmetry and division algebras

• Freudenthal magic square

• moonshine

  • Mathieu moonshine

  • umbral moonshine

  • O'Nan moonshine

Applications

• exceptional geometry, exceptional generalized geometry,

• exceptional field theory

Philosophy

• universal exceptionalism