22Dxx Locally compact groups and their representations
This subtopic studies locally compact groups and their representations, including nonabelian harmonic analysis and the interaction between topology and unitary representation theory.
Specific topics
22D05 General properties and structure of locally compact groups
Overview
22D05 studies general properties and structure of locally compact groups in locally compact groups and their representations. It studies locally compact groups together with representation-theoretic methods, especially unitary representations and harmonic analysis.
Related Wikipedia Page
Locally Compact Groups And Their Representations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general properties and structure of locally compact groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to connect topological group structure with representation theory and Fourier analysis.
Applications
- Unitary representation theory
- Harmonic analysis
- Structure theory for locally compact groups
References
Recommended Textbooks
22D10 Unitary representations of locally compact groups
Overview
22D10 studies unitary representations of locally compact groups in locally compact groups and their representations. It studies locally compact groups together with representation-theoretic methods, especially unitary representations and harmonic analysis.
Related Wikipedia Page
Locally Compact Groups And Their Representations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for unitary representations of locally compact groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to connect topological group structure with representation theory and Fourier analysis.
Applications
- Unitary representation theory
- Harmonic analysis
- Structure theory for locally compact groups
References
Recommended Textbooks
22D12 Other representations of locally compact groups
Overview
22D12 studies other representations of locally compact groups in locally compact groups and their representations. It studies locally compact groups together with representation-theoretic methods, especially unitary representations and harmonic analysis.
Related Wikipedia Page
Locally Compact Groups And Their Representations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other representations of locally compact groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to connect topological group structure with representation theory and Fourier analysis.
Applications
- Unitary representation theory
- Harmonic analysis
- Structure theory for locally compact groups
References
Recommended Textbooks
22D15 Group algebras of locally compact groups
Overview
22D15 studies group algebras of locally compact groups in locally compact groups and their representations. It studies locally compact groups together with representation-theoretic methods, especially unitary representations and harmonic analysis.
Related Wikipedia Page
Locally Compact Groups And Their Representations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for group algebras of locally compact groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to connect topological group structure with representation theory and Fourier analysis.
Applications
- Unitary representation theory
- Harmonic analysis
- Structure theory for locally compact groups
References
Recommended Textbooks
22D20 Representations of group algebras
Overview
22D20 studies representations of group algebras in locally compact groups and their representations. It studies locally compact groups together with representation-theoretic methods, especially unitary representations and harmonic analysis.
Related Wikipedia Page
Locally Compact Groups And Their Representations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of group algebras
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to connect topological group structure with representation theory and Fourier analysis.
Applications
- Unitary representation theory
- Harmonic analysis
- Structure theory for locally compact groups
References
Recommended Textbooks
22D25 $C^*$-algebras and $W^*$-algebras in relation to group representations
Overview
22D25 studies $c^*$-algebras and $w^*$-algebras in relation to group representations in locally compact groups and their representations. It studies locally compact groups together with representation-theoretic methods, especially unitary representations and harmonic analysis.
Related Wikipedia Page
Locally Compact Groups And Their Representations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for $c^*$-algebras and $w^*$-algebras in relation to group representations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to connect topological group structure with representation theory and Fourier analysis.
Applications
- Unitary representation theory
- Harmonic analysis
- Structure theory for locally compact groups
References
Recommended Textbooks
22D30 Induced representations for locally compact groups
Overview
22D30 studies induced representations for locally compact groups in locally compact groups and their representations. It studies locally compact groups together with representation-theoretic methods, especially unitary representations and harmonic analysis.
Related Wikipedia Page
Locally Compact Groups And Their Representations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for induced representations for locally compact groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to connect topological group structure with representation theory and Fourier analysis.
Applications
- Unitary representation theory
- Harmonic analysis
- Structure theory for locally compact groups
References
Recommended Textbooks
22D35 Duality theorems for locally compact groups
Overview
22D35 studies duality theorems for locally compact groups in locally compact groups and their representations. It studies locally compact groups together with representation-theoretic methods, especially unitary representations and harmonic analysis.
Related Wikipedia Page
Locally Compact Groups And Their Representations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for duality theorems for locally compact groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to connect topological group structure with representation theory and Fourier analysis.
Applications
- Unitary representation theory
- Harmonic analysis
- Structure theory for locally compact groups
References
Recommended Textbooks
22D40 Ergodic theory on groups; subgroup lattices
Overview
22D40 studies ergodic theory on groups; subgroup lattices in locally compact groups and their representations. It studies locally compact groups together with representation-theoretic methods, especially unitary representations and harmonic analysis.
Related Wikipedia Page
Locally Compact Groups And Their Representations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for ergodic theory on groups; subgroup lattices
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to connect topological group structure with representation theory and Fourier analysis.
Applications
- Unitary representation theory
- Harmonic analysis
- Structure theory for locally compact groups
References
Recommended Textbooks
22D45 Automorphism groups of locally compact groups
Overview
22D45 studies automorphism groups of locally compact groups in locally compact groups and their representations. It studies locally compact groups together with representation-theoretic methods, especially unitary representations and harmonic analysis.
Related Wikipedia Page
Locally Compact Groups And Their Representations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for automorphism groups of locally compact groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to connect topological group structure with representation theory and Fourier analysis.
Applications
- Unitary representation theory
- Harmonic analysis
- Structure theory for locally compact groups
References
Recommended Textbooks