Borel subgroup
E1438706
UNEXPLORED
A Borel subgroup is a maximal connected solvable algebraic subgroup of a linear algebraic group, playing a central role in the structure and representation theory of such groups.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Borel subgroups | 2 |
| Borel subgroup canonical | 1 |
| Borel subgroup of upper triangular invertible matrices | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T20563930 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Borel subgroup Context triple: [Borel–Weil theorem, usesConcept, Borel subgroup]
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A.
Borel subalgebras
Borel subalgebras are maximal solvable subalgebras of a Lie algebra that play a central role in the classification and representation theory of Lie algebras and algebraic groups.
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B.
Bruhat decomposition
Bruhat decomposition is a fundamental result in algebraic group theory that expresses a group as a union of double cosets indexed by elements of its Weyl group, revealing a deep combinatorial structure.
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C.
Lie subgroup
A Lie subgroup is a subgroup of a Lie group that is itself a Lie group and an embedded submanifold, inheriting compatible smooth and group structures from the ambient Lie group.
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D.
Fitting subgroup
The Fitting subgroup is a characteristic subgroup of a finite group formed by the product of all its nilpotent normal subgroups, playing a central role in the structure theory of finite groups.
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E.
Weyl group
A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Borel subgroup Target entity description: A Borel subgroup is a maximal connected solvable algebraic subgroup of a linear algebraic group, playing a central role in the structure and representation theory of such groups.
-
A.
Borel subalgebras
Borel subalgebras are maximal solvable subalgebras of a Lie algebra that play a central role in the classification and representation theory of Lie algebras and algebraic groups.
-
B.
Bruhat decomposition
Bruhat decomposition is a fundamental result in algebraic group theory that expresses a group as a union of double cosets indexed by elements of its Weyl group, revealing a deep combinatorial structure.
-
C.
Lie subgroup
A Lie subgroup is a subgroup of a Lie group that is itself a Lie group and an embedded submanifold, inheriting compatible smooth and group structures from the ambient Lie group.
-
D.
Fitting subgroup
The Fitting subgroup is a characteristic subgroup of a finite group formed by the product of all its nilpotent normal subgroups, playing a central role in the structure theory of finite groups.
-
E.
Weyl group
A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
- F. None of above. chosen
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Borel subgroup
subject linked to:
general linear group GL(n,C)
linked to: Borel subgroup
linked to: Borel subgroup