Lorentz group
E32549
Lie group
mathematical group
matrix group
non-abelian group
non-compact group
real Lie group
symmetry group
The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
All labels observed (11)
| Label | Occurrences |
|---|---|
| Lorentz group canonical | 7 |
| Lorentz invariance | 6 |
| SO^+(3,1) | 3 |
| Lorentz group SO(1,d-1) | 1 |
| Lorentz group in 3+1 dimensions | 1 |
| O(1,3) | 1 |
| SO(3,1) | 1 |
| orthochronous Lorentz group | 1 |
| proper Lorentz group | 1 |
| proper orthochronous Lorentz group | 1 |
| proper orthochronous Lorentz group SO^+(1,3) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T244298 — 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: Lorentz group Context triple: [Lorentz transformation, associatedWith, Lorentz group]
-
A.
Poincaré group
The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
-
B.
Lorentz transformation
The Lorentz transformation is a set of equations in special relativity that relate space and time coordinates between two inertial reference frames moving at a constant velocity relative to each other, ensuring the constancy of the speed of light.
-
C.
Minkowski space-time
Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
-
D.
Noether's theorem
Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
-
E.
Lorentz contraction
Lorentz contraction is the special relativistic effect in which an object’s length along the direction of motion appears shortened to observers in a different inertial frame moving at high relative velocity.
- 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: Lorentz group Target entity description: The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
-
A.
Poincaré group
The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
-
B.
Lorentz transformation
The Lorentz transformation is a set of equations in special relativity that relate space and time coordinates between two inertial reference frames moving at a constant velocity relative to each other, ensuring the constancy of the speed of light.
-
C.
Minkowski space-time
Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
-
D.
Noether's theorem
Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
-
E.
Lorentz contraction
Lorentz contraction is the special relativistic effect in which an object’s length along the direction of motion appears shortened to observers in a different inertial frame moving at high relative velocity.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
Lie group
ⓘ
mathematical group ⓘ matrix group ⓘ non-abelian group ⓘ non-compact group ⓘ real Lie group ⓘ symmetry group ⓘ |
| actsOn |
Minkowski space-time
ⓘ
surface form:
Minkowski spacetime
|
| definedBy | linear transformations preserving Minkowski bilinear form ⓘ |
| definedOn | four-dimensional real vector space ⓘ |
| hasAlternativeName |
Lorentz transformation
ⓘ
surface form:
Lorentz transformations
Lorentz group ⓘ
surface form:
O(1,3)
|
| hasApplicationIn |
general relativity (local tangent spaces)
ⓘ
high-energy physics ⓘ particle physics ⓘ |
| hasComponent |
connected component of identity
ⓘ
four connected components ⓘ |
| hasCoveringGroup | SL(2,C) ⓘ |
| hasDimension | 6 ⓘ |
| hasGenerator |
boost generators
ⓘ
rotation generators ⓘ |
| hasInvariant |
light cone structure
ⓘ
spacetime interval ⓘ |
| hasLieAlgebra | so(1,3) ⓘ |
| hasProperty |
non-compact simple Lie group up to discrete factors
ⓘ
not simply connected ⓘ |
| hasRank | 1 ⓘ |
| hasSignature | (1,3) ⓘ |
| hasSubgroup |
boost subgroup
ⓘ
Lorentz group self-linksurface differs ⓘ
surface form:
orthochronous Lorentz group
Lorentz group self-linksurface differs ⓘ
surface form:
proper Lorentz group
Lorentz group self-linksurface differs ⓘ
surface form:
proper orthochronous Lorentz group SO^+(1,3)
rotation group SO(3) ⓘ spatial rotation subgroup ⓘ |
| isIsomorphicTo | SO^+(1,3) ⓘ |
| isLocallyIsomorphicTo | SL(2,C) ⓘ |
| isSubgroupOf | Poincaré group ⓘ |
| namedAfter | Hendrik Lorentz ⓘ |
| preserves |
Minkowski space-time
ⓘ
surface form:
Minkowski metric
Minkowski spacetime interval ⓘ speed of light ⓘ |
| relatedTo |
Dirac equation
ⓘ
relativistic quantum field theory ⓘ representation theory ⓘ special relativity ⓘ spinors ⓘ |
| usedIn |
Poincaré group
ⓘ
surface form:
Wigner classification
classification of elementary particles ⓘ formulation of relativistic invariance ⓘ gauge theories ⓘ |
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: Lorentz group Description of subject: The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
Referenced by (24)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Lorentz invariance
this entity surface form:
Lorentz invariance
this entity surface form:
proper orthochronous Lorentz group
this entity surface form:
proper Lorentz group
this entity surface form:
orthochronous Lorentz group
this entity surface form:
proper orthochronous Lorentz group SO^+(1,3)
this entity surface form:
O(1,3)
subject surface form:
Hendrik Lorentz
this entity surface form:
Lorentz invariance
this entity surface form:
Lorentz invariance
this entity surface form:
Lorentz group SO(1,d-1)
this entity surface form:
Lorentz invariance
this entity surface form:
SO^+(3,1)
this entity surface form:
SO^+(3,1)
this entity surface form:
Lorentz group in 3+1 dimensions
this entity surface form:
SO(3,1)
this entity surface form:
SO^+(3,1)
this entity surface form:
Lorentz invariance