This is a list of things named after Sophus Lie. Sophus Lie (1842 – 1899), a mathematician, is the eponym of all of the things (and topics) listed below.
- Carathéodory–Jacobi–Lie theorem
- Lie algebra
- Lie-* algebra
- Lie algebra bundle
- Lie algebra cohomology
- Lie algebra representation
- Lie algebroid
- Lie bialgebra
- Lie coalgebra
- Lie conformal algebra
- Lie superalgebra
- Abelian Lie algebra
- Affine Lie algebra
- Anyonic Lie algebra
- Compact Lie algebra
- Complex Lie algebra
- Exceptional Lie algebra
- Finite-dimensional and infinite-dimensional Lie algebras
- Free Lie algebra
- Graded Lie algebra
- Homotopy Lie algebra
- Malcev Lie algebra
- Modular Lie algebra
- Monster Lie algebra
- Nilpotent Lie algebra
- Nilradical of a Lie algebra
- Orthogonal symmetric Lie algebra
- Parabolic Lie algebra
- Pre-Lie algebra
- Quadratic Lie algebra
- Quasi-Frobenius Lie algebra
- Quasi-Lie algebra
- Real Lie algebras
- Reductive Lie algebra
- Restricted Lie algebra
- Semisimple Lie algebra
- Split Lie algebra
- Symplectic Lie algebra
- Tangent Lie group
- Tate Lie algebra
- Toral Lie algebra
- Lie bracket of vector fields
- Lie derivative
- Lie group
- Lie point symmetry
- Lie product formula
- Lie ring
- Lie sphere geometry
- Lie theory
- Lie–Kolchin theorem
- Lie–Palais theorem
- Lie's theorem
- Lie's third theorem
- Lie transform