Classification

Classification is a route into the atlas. It does not imply equal computational coverage for every classified object.

Finite simple groups

Read the finite-simple classification: the 18 infinite families, 26 sporadic groups, and separate Tits-group convention. Each family specifies parameters, small exceptions, and important identifications.

Complex simple Lie algebras and compact global forms

Read the Lie classification: types A, B, C, D, E₆, E₇, E₈, F₄, and G₂; rank restrictions and compact central quotients.

Real forms

Read the curated real-form index: the local real algebra, its complexification, and the selected integrating groups. The current real-form index is scoped; it is not a complete noncompact unitary representation classification.

Beyond simplicity

Groups used in physics also include products, covers, quotients, and non-simple groups. Browse finite symmetries, gauge groups, or spacetime groups to enter by a physical problem.