Lie ring
E140808
A Lie ring is an algebraic structure consisting of an abelian group equipped with a bilinear, alternating, and Jacobi-identity-satisfying bracket operation, serving as the ring-theoretic analogue of a Lie algebra.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Jacobi identity | 1 |
| Lie ring canonical | 1 |
| Zassenhaus group | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1234896 — 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: Lie ring Context triple: [Sophus Lie, hasConceptNamedAfter, Lie ring]
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A.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
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B.
Weyl
Weyl is a surname most famously associated with Hermann Weyl, a prominent 20th-century mathematician and theoretical physicist known for major contributions to group theory, quantum mechanics, and the foundations of mathematics.
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C.
Abelian groups
Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
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D.
Noether's isomorphism theorems
Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
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E.
Lie theory
Lie theory is a branch of mathematics that studies continuous symmetry through Lie groups and Lie algebras, with deep applications in geometry, analysis, and theoretical physics.
- 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: Lie ring Target entity description: A Lie ring is an algebraic structure consisting of an abelian group equipped with a bilinear, alternating, and Jacobi-identity-satisfying bracket operation, serving as the ring-theoretic analogue of a Lie algebra.
-
A.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
-
B.
Weyl
Weyl is a surname most famously associated with Hermann Weyl, a prominent 20th-century mathematician and theoretical physicist known for major contributions to group theory, quantum mechanics, and the foundations of mathematics.
-
C.
Abelian groups
Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
-
D.
Noether's isomorphism theorems
Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
-
E.
Lie theory
Lie theory is a branch of mathematics that studies continuous symmetry through Lie groups and Lie algebras, with deep applications in geometry, analysis, and theoretical physics.
- F. None of above. chosen
Statements (48)
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: Lie ring Description of subject: A Lie ring is an algebraic structure consisting of an abelian group equipped with a bilinear, alternating, and Jacobi-identity-satisfying bracket operation, serving as the ring-theoretic analogue of a Lie algebra.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Jacobi identity
this entity surface form:
Zassenhaus group