Group theory and generalizations Linear and matrix groups Concept
Linear algebraic group
Summary
A linear algebraic group is a group of invertible matrices defined by polynomial equations in the entries. Equivalently, it is an algebraic group whose underlying scheme is affine. Examples are the general linear group, the special linear group, the orthogonal groups and the symplectic groups. Their structure theory, through tori, Borel subgroups and root systems, is a large part of modern algebra and number theory.
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Further reading
About this page
| Tag | GA81VVQHEP |
|---|---|
| URI | m2://GA81VVQHEP |
| Kind | concept |
| Writing | W0 stub |
| MSC | 20G15, 14L17 |
| Specializes | Algebraic group |
| Same as | |
| Changed | 2 November 2026 |
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Special cases
Used by
- Borel–Harish-Chandra theorem
- Algebraic torus
- Margulis arithmeticity theorem
- Borel fixed-point theorem
- Chevalley's structure theorem
- Borel subgroup
- Reductive group