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Canonical static concept record

Lorentz group

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Summary

The group preserving a nondegenerate quadratic form of Lorentzian signature.

Record metadata

Carrier(s)

Data

Axioms / constraints

Canonically induces

Notes

“Lorentz group” may denote the full group O(1,3)O(1,3) or a specified subgroup such as SO+(1,3)SO^+(1,3).

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Lie groupLorentz group

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

The Lorentz group is the Lie group preserving a Lorentzian quadratic form.

How to interpret this relation type

A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Lorentz groupLorentz symmetry

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Lorentz symmetry is mathematically represented by the Lorentz group.

How to interpret this relation type

A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.

Relation sources

Lorentz groupPoincaré group

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

For a fixed Minkowski vector space, the Poincaré group is the semidirect product of spacetime translations with the Lorentz group.

How to interpret this relation type

Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.

Relation sources