Departure question
Move sameness aroundPort 3 of 8Use rotations, permutations, matrices, and categories to read transformation rules and relationships rather than appearances.
This voyage is an editorial path for understanding, not a claim of direct historical influence or sole invention.
Groups of continuously varying symmetries. Rotation groups such as SO(3), the Lorentz group, and gauge symmetries appear throughout geometry and theoretical physics. Lie algebras, developed from Sophus Lie's program, linearize infinitesimal motion near the identity of a finite-dimensional Lie group. This local data is powerful, but it does not always determine the group's global topology.
Continuous symmetries — the language of modern particle physics and gauge theory.
Ports in time
Follow the scenes to see problems, notation, standards of proof, and applications changing across different times and places.
Sophus Lie generalized Galois’s discrete groups to continuous transformations and used their symmetries to study differential equations.
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Continue through the world of this yearÉlie Cartan’s work completed the classification of simple Lie algebras and illuminated the exceptional families G₂, F₄, E₆, E₇, and E₈.
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Continue through the world of this yearChen-Ning Yang and Robert Mills proposed a gauge theory based on non-commutative Lie groups, laying groundwork for the Standard Model.
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Continue through the world of this yearGell-Mann’s Eightfold Way and Ne’eman’s independent work organized hadrons through approximate SU(3) flavor symmetry. The later omega-minus discovery strongly supported the pattern.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearThe Standard Model of particle physics, general relativity, quantum field theory, robot pose control, and rotations in computer graphics.
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Number lenses
These numbers are editorial lenses for the voyage, not required prerequisites.
Use rotations, permutations, matrices, and categories to read transformation rules and relationships rather than appearances.
Open the number voyage
Use rotations, permutations, matrices, and categories to read transformation rules and relationships rather than appearances.
Open the number voyage
Use rotations, permutations, matrices, and categories to read transformation rules and relationships rather than appearances.
Open the number voyage
Concept genealogy
Concepts arriving from before
Current port
Lie Groups
Concepts opened from here
No direct successor port is curated yet.
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