Topological groups, Lie groups Locally compact groups and Haar measure Concept
Locally compact group
Summary
A locally compact group is a Hausdorff topological group whose topology is locally compact. These groups carry a Haar measure, an invariant way to measure and integrate, which makes harmonic analysis on them possible. They include all Lie groups, all discrete groups, all compact groups and the groups of points of algebraic groups over local fields such as .
Where this leads
25 pages build on this one.
- Harmonic analysis on groups
- Unitary dual
- Discrete series representation
- van Dantzig's theorem
- Cayley–Abels graph
- Induced representation of a locally compact group
- Hecke algebra of a locally compact group
- Group C*-algebra
- Mackey machine
- Group von Neumann algebra
- Lattice in a locally compact group
- Haar measure
- Gelfand–Raikov theorem
- Weil's converse to Haar's theorem
- Mackey imprimitivity theorem
- Plancherel theorem for groups
- Group algebra of a locally compact group
- Hilbert–Smith conjecture
- Haagerup property
- Gelfand pair
- Convolution
- Filtered back-projection
- Modular function
- Gleason–Yamabe theorem
- Unimodular group
Further reading
About this page
| Tag | AHV05ZBCYW |
|---|---|
| URI | m2://AHV05ZBCYW |
| Kind | concept |
| Writing | W0 stub |
| MSC | 22D05, 22A05 |
| Specializes | Hausdorff topological group |
| Same as |
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What links here
Used by
- Harmonic analysis on groups
- Unitary dual
- Discrete series representation
- van Dantzig's theorem
- Cayley–Abels graph
- Induced representation of a locally compact group
- Hecke algebra of a locally compact group
- Group C*-algebra
- Mackey machine
- Group von Neumann algebra
- Lattice in a locally compact group
- Haar measure
- Gelfand–Raikov theorem
- Weil's converse to Haar's theorem
- Mackey imprimitivity theorem
- Plancherel theorem for groups
- Group algebra of a locally compact group
- Hilbert–Smith conjecture
- Haagerup property
- Gelfand pair
- Convolution
- Modular function
- Gleason–Yamabe theorem
- Unimodular group
Definitions
Results about this
- Gelfand–Raikov theorem
- Weil's converse to Haar's theorem
- Hilbert–Smith conjecture
- Gleason–Yamabe theorem