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Canonical static concept record

Compact Lie group

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Summary

A Lie group whose underlying topological space is compact.

Record metadata

Carrier(s)

Data

Axioms / constraints

Canonically induces

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Lie groupCompact Lie group

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

Authored explanation

A compact Lie group has compact underlying topology.

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Compact Lie groupCircle group U(1)U(1)

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

Authored explanation

The circle group is the compact one-dimensional unitary group.

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

Compact Lie groupSpecial unitary group

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

Authored explanation

The special unitary groups are compact matrix Lie groups.

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