20Hxx Matrix groups
This subtopic studies matrix groups, including classical matrix groups and their algebraic and geometric properties.
Specific topics
20H05 Unimodular groups, congruence subgroups of matrix groups
Overview
20H05 studies unimodular groups, congruence subgroups of matrix groups in matrix groups. It studies groups realized as invertible matrices, emphasizing classical, arithmetic, and geometric subclasses.
Related Wikipedia Page
Matrix Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for unimodular groups, congruence subgroups of matrix 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 linear actions with geometry, arithmetic, and subgroup structure.
Applications
- Classical matrix groups
- Arithmetic and geometric matrix groups
- Structure and subgroup analysis
References
Recommended Textbooks
20H10 Fuchsian groups and their generalizations
Overview
20H10 studies fuchsian groups and their generalizations in matrix groups. It studies groups realized as invertible matrices, emphasizing classical, arithmetic, and geometric subclasses.
Related Wikipedia Page
Matrix Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for fuchsian groups and their generalizations
- 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 linear actions with geometry, arithmetic, and subgroup structure.
Applications
- Classical matrix groups
- Arithmetic and geometric matrix groups
- Structure and subgroup analysis
References
Recommended Textbooks
20H15 Other geometric groups, including crystallographic groups
Overview
20H15 studies other geometric groups, including crystallographic groups in matrix groups. It studies groups realized as invertible matrices, emphasizing classical, arithmetic, and geometric subclasses.
Related Wikipedia Page
Matrix Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other geometric groups, including crystallographic 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 linear actions with geometry, arithmetic, and subgroup structure.
Applications
- Classical matrix groups
- Arithmetic and geometric matrix groups
- Structure and subgroup analysis
References
Recommended Textbooks
20H20 Other matrix groups over fields
Overview
20H20 studies other matrix groups over fields in matrix groups. It studies groups realized as invertible matrices, emphasizing classical, arithmetic, and geometric subclasses.
Related Wikipedia Page
Matrix Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other matrix groups over fields
- 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 linear actions with geometry, arithmetic, and subgroup structure.
Applications
- Classical matrix groups
- Arithmetic and geometric matrix groups
- Structure and subgroup analysis
References
Recommended Textbooks
20H25 Other matrix groups over rings
Overview
20H25 studies other matrix groups over rings in matrix groups. It studies groups realized as invertible matrices, emphasizing classical, arithmetic, and geometric subclasses.
Related Wikipedia Page
Matrix Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other matrix groups over rings
- 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 linear actions with geometry, arithmetic, and subgroup structure.
Applications
- Classical matrix groups
- Arithmetic and geometric matrix groups
- Structure and subgroup analysis
References
Recommended Textbooks
20H30 Linear groups over specific rings
Overview
20H30 studies linear groups over specific rings in matrix groups. It studies groups realized as invertible matrices, emphasizing classical, arithmetic, and geometric subclasses.
Related Wikipedia Page
Matrix Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for linear groups over specific rings
- 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 linear actions with geometry, arithmetic, and subgroup structure.
Applications
- Classical matrix groups
- Arithmetic and geometric matrix groups
- Structure and subgroup analysis
References
Recommended Textbooks