# Physics Notes by Jakob Schwichtenberg

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group_theory:notions:lie_groups

# Lie Group

A Lie group is a continuous set of transformations that satisfy the group axioms. A good example for a Lie group is the symmetry group of the circle. A rotation by $5^\circ$ is a symmetry of the circle and a rotation by $0.00001^\circ$ is a symmetry, too. In contrast, the symmetry group of a square is not continuous. A rotation by $90^\circ$ is a symmetry, whereas a rotation by $5^\circ$ is not a symmetry.

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