Knapp, Anthony W. Department of Mathematics, State University of New York, Stony Brook, New York.
Last reviewed:January 2020
- Examples of Lie groups
- Lie algebra
- Abstract Lie algebras
- Analytic subgroups
- Exponential map
- Fourier analysis
- Sample applications
- Rotations and the Fourier transform
- Solutions of differential equations
- Quantum mechanics
- Related Primary Literature
- Additional Reading
A topological group with only countably many connected components whose identity component is open and is an analytic group. An analytic group or connected Lie group is a topological group with the additional structure of a smooth manifold such that multiplication and inversion are smooth. Many groups that arise naturally as groups of symmetries of physical or mathematical systems are Lie groups. The study of Lie groups has applications to analytic function theory, differential equations, differential geometry, Fourier analysis, algebraic number theory, algebraic geometry, quantum mechanics, relativity, and elementary particle theory. See also: Group theory; Manifold (mathematics); Topology
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