22Exx Lie groups
This subtopic studies Lie groups, connecting smooth manifold structure with group actions, differential geometry, and representation theory.
Specific topics
22E05 Local Lie groups
Overview
22E05 studies local lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for local lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E10 General properties and structure of complex Lie groups
Overview
22E10 studies general properties and structure of complex lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general properties and structure of complex lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E15 General properties and structure of real Lie groups
Overview
22E15 studies general properties and structure of real lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general properties and structure of real lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E20 General properties and structure of other Lie groups
Overview
22E20 studies general properties and structure of other lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general properties and structure of other lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E25 Nilpotent and solvable Lie groups
Overview
22E25 studies nilpotent and solvable lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for nilpotent and solvable lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E27 Representations of nilpotent and solvable Lie groups
Overview
22E27 studies representations of nilpotent and solvable lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of nilpotent and solvable lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E30 Analysis on real and complex Lie groups
Overview
22E30 studies analysis on real and complex lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for analysis on real and complex lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E35 Analysis on $p$-adic Lie groups
Overview
22E35 studies analysis on $p$-adic lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for analysis on $p$-adic lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E40 Discrete subgroups of Lie groups
Overview
22E40 studies discrete subgroups of lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for discrete subgroups of lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E41 Continuous cohomology of Lie groups
Overview
22E41 studies continuous cohomology of lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for continuous cohomology of lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E43 Structure and representation of the Lorentz group
Overview
22E43 studies structure and representation of the lorentz group in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for structure and representation of the lorentz group
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E45 Representations of Lie and linear algebraic groups over real fields
Overview
22E45 studies representations of lie and linear algebraic groups over real fields in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of lie and linear algebraic groups over real fields
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E46 Semisimple Lie groups and their representations
Overview
22E46 studies semisimple lie groups and their representations in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for semisimple lie groups and their representations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E47 Representations of Lie and real algebraic groups: algebraic methods
Overview
22E47 studies representations of lie and real algebraic groups: algebraic methods in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of lie and real algebraic groups: algebraic methods
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E50 Representations of Lie and linear algebraic groups over local fields
Overview
22E50 studies representations of lie and linear algebraic groups over local fields in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of lie and linear algebraic groups over local fields
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E55 Representations of Lie and linear algebraic groups over global fields
Overview
22E55 studies representations of lie and linear algebraic groups over global fields in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of lie and linear algebraic groups over global fields
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E60 Lie algebras of Lie groups
Overview
22E60 studies lie algebras of lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for lie algebras of lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E65 Infinite-dimensional Lie groups and their Lie algebras
Overview
22E65 studies infinite-dimensional lie groups and their lie algebras in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for infinite-dimensional lie groups and their lie algebras
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E66 Analysis on and representations of infinite-dimensional Lie groups
Overview
22E66 studies analysis on and representations of infinite-dimensional lie groups in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for analysis on and representations of infinite-dimensional lie groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E67 Loop groups and related constructions
Overview
22E67 studies loop groups and related constructions in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for loop groups and related constructions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks
22E70 Applications of Lie groups to the sciences; explicit representations
Overview
22E70 studies applications of lie groups to the sciences; explicit representations in Lie groups. It studies smooth groups and their infinitesimal Lie algebraic structure, linking analysis, geometry, and representation theory.
Related Wikipedia Page
Lie Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for applications of lie groups to the sciences; explicit representations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in differential geometry, Lie theory, and the study of continuous symmetry.
Applications
- Continuous symmetry in geometry and physics
- Lie algebra correspondence
- Representation theory of smooth groups
References
Recommended Textbooks