Tits building
E921614
A Tits building is a highly structured combinatorial and geometric object that encodes the incidence relations of subspaces or parabolic subgroups associated with a reductive algebraic or Lie group.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Tits building canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11365358 — 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: Tits building Context triple: [Deligne–Lusztig theory, relatesTo, Tits building]
-
A.
Titans Tower
Titans Tower is the iconic T-shaped headquarters of the Teen Titans, serving as their primary base and living quarters in DC Comics.
-
B.
Broel Towers
Broel Towers are a pair of medieval defensive towers and an iconic historical symbol of the Belgian city of Kortrijk (Courtrai).
-
C.
Tektite Towers
Tektite Towers is a prominent twin-tower office complex in Ortigas Center, Metro Manila, known for housing the Philippine Stock Exchange offices for many years.
-
D.
Ubora Towers
Ubora Towers is a prominent pair of modern high-rise office and residential buildings located in Dubai’s Business Bay district.
-
E.
Lollipop Building
The Lollipop Building is a distinctive mid-20th-century modernist structure in Manhattan known for its controversial, ornamented façade and later renovation into the Museum of Arts and Design.
- 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: Tits building Target entity description: A Tits building is a highly structured combinatorial and geometric object that encodes the incidence relations of subspaces or parabolic subgroups associated with a reductive algebraic or Lie group.
-
A.
Titans Tower
Titans Tower is the iconic T-shaped headquarters of the Teen Titans, serving as their primary base and living quarters in DC Comics.
-
B.
Broel Towers
Broel Towers are a pair of medieval defensive towers and an iconic historical symbol of the Belgian city of Kortrijk (Courtrai).
-
C.
Tektite Towers
Tektite Towers is a prominent twin-tower office complex in Ortigas Center, Metro Manila, known for housing the Philippine Stock Exchange offices for many years.
-
D.
Ubora Towers
Ubora Towers is a prominent pair of modern high-rise office and residential buildings located in Dubai’s Business Bay district.
-
E.
Lollipop Building
The Lollipop Building is a distinctive mid-20th-century modernist structure in Manhattan known for its controversial, ornamented façade and later renovation into the Museum of Arts and Design.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial structure
ⓘ
geometric structure ⓘ mathematical object ⓘ |
| appliesTo |
Chevalley group
NERFINISHED
ⓘ
classical group ⓘ exceptional algebraic group ⓘ |
| arisesFrom |
flags of subspaces in a vector space
ⓘ
parabolic subgroups of a reductive group ⓘ |
| associatedWith |
reductive Lie group
ⓘ
reductive algebraic group ⓘ |
| characterizedBy |
Weyl distance function
ⓘ
apartment system ⓘ strong transitivity of automorphism group ⓘ |
| definedBy | axioms of incidence geometry ⓘ |
| encodes |
incidence relations
ⓘ
parabolic subgroup structure ⓘ subspace incidence ⓘ |
| field |
Lie theory
ⓘ
algebraic geometry ⓘ group theory ⓘ incidence geometry ⓘ |
| generalizes |
flag complex of a vector space
ⓘ
projective space incidence structure ⓘ |
| hasComponent |
Weyl group
NERFINISHED
ⓘ
apartment ⓘ chamber ⓘ panel ⓘ |
| hasProperty |
highly symmetric
ⓘ
homogeneous under automorphism group ⓘ |
| hasType |
affine building
ⓘ
hyperbolic building ⓘ spherical building ⓘ |
| introducedBy | Jacques Tits NERFINISHED ⓘ |
| namedAfter | Jacques Tits NERFINISHED ⓘ |
| relatedTo |
BN-pair
ⓘ
Coxeter system NERFINISHED ⓘ affine building ⓘ root system ⓘ spherical building ⓘ |
| studiedIn |
geometric group theory
ⓘ
representation theory ⓘ |
| usedFor |
classification of semisimple algebraic groups
ⓘ
classification of simple algebraic groups ⓘ study of BN-pairs ⓘ |
| usedIn |
proofs of classification of simple groups of Lie type
ⓘ
study of arithmetic groups ⓘ study of p-adic Lie groups ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Tits building Description of subject: A Tits building is a highly structured combinatorial and geometric object that encodes the incidence relations of subspaces or parabolic subgroups associated with a reductive algebraic or Lie group.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.